Taylor, E S

English

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'3!IC3KCCAL fOTES 
-u- -- - 
No. 533 
TIT!2 T3BR~ODYNAMIC8 OF t2OMBTJSTIOd 
By E. S. Taylor 
llassachusetts Tnstitute of TWhnOlOgg -- 
, , - . . : . . _ _. 
Washhington 
June 1935 
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NATIONAL ADVISORY COMEITTEI FOR AXXOBAUTICS 
d-P 
.- 
TECHRICAL XOTE NO. 533 
----- 
TRY! THERMODYWAXICS OF COMBUSTION 
I?!? THD OTTO CYCLE.l!XGINE 
By 1. S. Taylor 
In thermodynamic analyses of the Otto cycle, the com- 
bustion process is normally dismissed with the sentence 
"heat is add& at constant v01ume.*~ 
As early as 1906, HoDkinson (reference 1) indicated 
the thermodynamZc nature of the process of combustion by 
experEment5 in a closed vessel. In 1934, Lewis and van 
Elbe (reference 2) took up thfs work, and showed very con- 
clusfvely the nature of "constant-vofune" combustion in a 
closed vessel. There has been rather a widespread feeling, 
however, that the combustion process in an engine might be 
essentially different from that in a bomb because of the 
part played by turbulence in spreading the flame. 
Recent experiments by Bassweiler and TPithrow (refer- 
ence 3) indicate what might have been predicted from pre- 
viously available evidence, i.e., the essential similarf- 
ty of the combustion process in engtlnes and enclose& vcs- 
sels. Turbulence is, of ccurse, extremely effective in 
equalizing any existing temperature differences that may 
momentarily extst in the cylinder but, since the rate Of . 
flame propagation depends on the transfer of heat from the 
burned to the unburned gas, . turbulence is ecuallYef.fec- 
tive in increasing ------- the flame velocity. 
The evidence presented by Bassweiler and Withrow in- 
dicates a temperature difference exfsting in the cylinder 
immediately after combustion of about 600' F. The nature 
of the measurement leads one to believe that the actual 
temperature difference is somewhat greater than the mcas- 
ureh difference because of 
i 
al the use of a stroboscopic method with a phenome- 
non that does not repeat exactly, T 
b) the practical difficulty, with the sodium-line 
reversal method, of measuring average temperatures at . 
2 iVN,B,C.A. Technical Note No. 533 
points within a given volume (i..e,, the flame front) with- 
out including points outside this volume, and 
4 the fmpossibility of getting instantaneous values 
with the consequent necessfty for accepting time averages, 
Because of theso faotors, the sxperfmental values,of 
the temperature difference may be said to represent the 
lower limit of this quantity. It Is quite simple to de- 
termine an upper limit by analysis and, in addition, the 
analytical method clarifies the picture of the process~ 
In order to represent mathematically any physioal 
phenomenon, oertaln simplifying assumptions must bo made. 
For the purpose of calculation, we shall make the follow- 
ing assumptLons, discussing the degree of approximation 
to actual conditions later: 
(1) The worki ng medium is a perfect gas. 
(2) The piston motion during combustion is negligPble, 
(3) At any Instant, the pressure in all parts of the 
cylinder is the samee 
(4) The combusti on process reqairas a finite time. 
(5) Heat is added to the working flufd on& at the - 
flame front, 
(6) The heat transfer within the gas during the com- 
bustion process is negligible** 
Assumptions (l), (B), and (3) are the assumptions or- 
dinarily made for perfect gas cycles. 
fact, 
Statement (4) is 'not an assumption but an observed 
Assumptions (5) and (6) are those made by LOWI? and 
van Elbe (reference 2) and are useful for the slmplLfi.ca- 
tion of the reasoning that follows from the consideration 
of a finite combustion time. 
w-----h-- ---- -- * 
A somewhat similar analysS.s, but based upon isothermal 
compression of the burned gases, 9s given in referenoc3 4, 
c 
X.A.C.A. Technical Note Xo. 533 3 
. 
Let us now consider the l'constant-volumelr cycle as 
represented by 1, 2, 3, and 4 in figure 1. Note that the 
abscissa scale is mecqftc volume (cu. ft. per lb.). --AZ. 
All of the gas in the cylinder is compressed from Pl, 
V.J. 'co P2, v2 and consequently at point 2 it is at a uni- 
form temperature,, T2. At point 2 ignition occurs at some 
definite point or points in the cylinder. -- . . -. 
Let us now consider what happens to a small volume of 
gas immediately adjacent to the pofnt of ignition, Sines 
combustion IS now considered to occupy a finite time, the 
medium occupyfng the small volume in question is free to 
exuand agatinst the unburned gas in the cylinder. If the 
volume chosen is inffnitesimal, it will expand without af- 
fecting tha general cylinder pressure. Thus heat is added 
to this small volume at constant .-----.y~s~~~ a:; k;zil;;rE-m 
pand to point 2.1 on the diagram 
proceeds, this small 'volume of gas will-be comp??es-sed to 
point 31 (adiabatically since ;pe are assuming no heat fn- 
torchange). It will then '30 re-expanded by the motion of 
the piston to the exhaust pressure.8 
If we consider now the last part of the charge to 
burn, we see that ft is compressed before combustion to the -----e 
maximum cyclitc pressure at point 2"!. The heat of combus- 
t1on then expands it (at constant pressure since it is 
small compared to the totgs=rne of gas) to point 3" 
whence it is expanded by the motion of the piston. -Simi- 
larly, any intermediate small vdlume of gas-will go through 
a cycle in which heat is added at some intermediate pres- 
sure level. Thus we see that the ltconstant-volume cycle" 
is really the resultant of the sum of an infinite number 
of different cycles in each of which heat is added at con- 
stant pressure, Te also observe that there is a differ- 
ence in specific volume and, therofore, in temperature 
from the last part of the charge to burn to the part near 
the egnition point, In order to inhicaYke the possible 
magnitude of thfs temperature difference; if 'has been cal- 
culated for an assumed case where the compression r.afio is 
5, . the inlet conditions are pl = X4.7, Tl = 600' F. a&l 
solute, cv =f 0,169, 6P = 0.238. Seat addedi 650 B.t.ua 
per pound of air. (This value was chosen to give approx- 
fmatel$ the pressures found in practice,) The tabulation 
below gjves the results of the calculation: 
l 
H.A.C.A. Technfcal Dots No, 533 
Point . P v T 
2 140 3.02 1140 
3 611 3-;-02 4990 
2' 140 10.2 3870 
2 II 611 1.05 1740 
3' 611 2.57 5900 
3" 611 2.71 447.0 
QI represonta tho tomperature near tho spark- plug 
after combustion is complete. T3' 3.6 some 1,500' F, 
higher than T31t, the temperature of the last part of the 
charge to burn at the same instant, 
This temperature gradient is the maximum that can ox- 
Zst under the circumstances. 
-----I 
The fact that there is heat 
transgcr within the gas during combustion ~511, of COU~SQ~ 
redxco the graditent. Ths gradient will aL6o be rcducod 
by the fact that heat is added not fn an infdnitesimallp 
thin layer at the flame front but in a layer of finite 
thickness. The change mith.temperature of the specfific 
hoat of the working fluid will likewise operate to reduce 
the temperature difforonco.* 
It will be noted that the effect of the change in 
specific heat and the effect of heat transfer upon the 
temperature gradient depend upon the existence of such a 
gradient and are, therefore, second-order effects. 
The thickness of the reaction zons and the duration 
of reaction at a point within the gas has been fnvestigat- 
sd by several different methods. 
mya, (referonce 5), 
Withrow, Lovell, and 
value of 17O 
using a sampling valve, show a maximum 
duratLon at 1,000 rlplmm The same investi,ga- 
tions in a later publication (reference 6) estimate from 
flame photographs that the reaction zone is from 3/8 to 
l* inches thick and has a duration of from 3 to 10 Crank- 
shaft degrees at 1,000 r#plmr Marvin (z-of orenc8 71, meas- 
uring ths radiation from the flame, estimates 22' duratfon 
at 1,000 r.p#m. All of this work is subject to crftioism 
as *o its accuracy and. it is probable that the estimates 
show only the order of magnitude of the duratfon and thick- 
ness of the reaction zone, The methods used, however, give 
----------------------~ --II_ 
*J. method of calculation, making allowance for- tho change 
in specific heat is given in reference 2, 
l 
. . 
‘N,A*C .A. Technical Mote X0. 533 5 
results that are likely to be greater than the actual val- 
U88, (See discussion, reference 3.) unaoub%8aiy, - oher-- 
atfng variables, especially the fuel-air rat&o and the 
turbulence, affect the thickness of the reactfon zone. 
Xore accurate fnformation 'ss needed on this point before 
the effect of a finite reaction-zone thickness can be ac- 
curately evaluated. 
. Since all the assumptions for our computation lead-to 
high values and since the exporfmental values* for reasons 
0utlin8a above, are low, the temperature difference ejc- --~ 
Esting inthe cylinder lies between the eqerimental 600' 
F, and the theoretical 1,500' 3. 
In the study of detonation the sodium-line reversal 
method of measuring temperatures is of lfttle value in in- 
d.fcatiing even an approximation to the actual conaition, 
.sinco the extremely high local pressure can only exist for 
n t&no tzlat is very short compared with the time necessary 
for maktng a measurement. Here again, it fs possible ana- 
lytically to establish upper limits on the temperature and 
pressure. . 
. 
It is now fairly well accepted that detonation is a 
rapid reaction fn the last part of the shargo to burn, 
probably fnitiated by compression ignZtion ahead of the 
flame front. If the reaction is suffioiently rapid, corn- 
bustion can no Longer bo at constant pressure but will ap- 
proach the conditions of constant volume, In the limZt- 
ing case of instantaneous combustion of the last part of 
the charge to.burn, the combustion fr0m.poin-t 2" at con- 
stant volume would cause a local pressure of 1,960 pounds 
per sc&uaro inch, with a oorrosponai=?g temperature of 
5,590 3. absolute. Owing to the increase in specific 
heat and the change fn chemEca1 equilibrium at high tempor- 
atures as rrall as to the fact that aombustion is never in- 
stantaneous, this pressure and temperature ~911 never be 
reache'a but they are the lemitfng values that may not be 
oxceeaea under the 00na5tionf3 0f our assumption. Although 
we ara dealing with approximations, the temperature of the 
gas participating fn detonation is probably lower, and 
Gertain3.y not very much higher, than the temperature else- 
where in the cylinder. Thuo, tt cannot be the high tern- 
pera.ture alone that causes the aestructive effects of deto- 
natlon but perhaps a oombination of 8xfrem8ly high pres- 
sures and i.ncreased local heat conduct%on d.ue to the high 
density of the detonating part of the charge. 
The Daniel Guggenheim Aeronautical Laboratory, 
Massachusetts Instftuts of Technology, 
Cambridge, Mass., April 16, 1935. 
1. 
3, 
3, 
4. 
5. 
6, 
7. 
N,A,C,A, Technfoal Note No, 533 
REFERENCES 
Hopkinson, B.: Explosions in Gaseous Idix~urea and 
the Specific Heat of th8 Products. Engineering, 
vol. 81, 1906, ps ,777, 
Lewis, Be, and van Elbe, G,: Determination of the 
Speed of Flames and the Temperature Distribution 
En a Spherical Bomb from Time-Pressure Explosion 
Records, Jour. of Chemical Physics, ~011 2, May 
1934, pm 283. 
Rassweiler, Gsrald M,, and Vithrow, Lloyd: Flame !I?Qm- 
peratures Vary with Knock and Combustion-Chamber 
Position. S.A.E. Jour., vol. 36, n-9. 4, April. 
1935, ppm 125-13-5. 
Mfdgely, Thomas, Jr., and Janeway, Robert: The PreS- 
sure-Volume-Quantity Indicator-Card. S,A,E. Trans,, 
Part I, 1923, ppa 77-943 
Withrow, Lloyd, ~0~811, IY. G., and Boyd, T. A.: Fol- 
lowing Combustion in the Gasoline Engine by Chem- 
ical Means, Ina. & Eng. ChQm,, vol. 22, noa 9, 
Ssptomber 1930, pp. 945-951, 
Vithrow, Lloyd, and Boyd, T, A.: Photographic Flame 
Studies in the Gasoline Engine. Ind. & Engr Chem,, 
vol. 23, no, 5, May 1931, pp. 539-547, 
Marvin, Charles F., Jr.: Obser%ations of Flame in an 
Engine. S,A,E. Jour., vol. 35, noa 5, NovembQr 
1934, pp. 391-398. 
N.A.C.A. Technical Bate ::o. 533 Fig. 1 
. . 
Speciffc volune 
Figure 1. 
, 


The thermodynamics of combustion in the Otto cycle engine

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