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800459

Cyclic Dispersion -
Some Quantitative
Cause-and-Effect Relationships
Michael B. Young
Engine Research Dept.
General Motors Research Labs.

Congress and Exposition

Cobo Halt, Detroit
February 25-29, 1980
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ISSN 0148-7191
C o p y r i g h t © 1980 S o c i e t y o f A u t o m o t i v e Engineers, I n c .
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800459

Cyclic Dispersion -
Some Quantitative
Cause-and-Effect Relationships
Michael B. Y o u n g
Engine Research Dept.
General Motors Research Labs.

MUCH WORK HAS BEEN DONE in the area of cycle-to- o p e r a t i n g c o n d i t i o n s and combustion chamber
cycle behavior of the homogeneous-charge spark- geometry on t h e n a t u r e o f e n g i n e c o m b u s t i o n , and
ignited engine [1-183". !n these studies many subsequently of the e f f e c t s of engine combustion
variables have been used to characterize cycle- c h a r a c t e r i s t i c s on engine s t a b i l i t y (IMEP
to-cycle variations. Flame arrival times [1-8], variability), is lacking. The o b j e c t i v e of this
mass burning rates [9-10], peak pressures s t u d y was t o h e l p f i l l this void. Vehicle
[11-l*f], maximum rates of pressure rise [15], d r i v e a b i l i t y p r o b l e m s c a n be a d d r e s s e d m o r e
crankangles of peak pressure [12], and indicated e f f e c t i v e l y when t h e r e l a t i o n s h i p between
mean e f f e c t i v e pressures (1MEP) [16-18] are combustion c h a r a c t e r i s t i c s and e n g i n e p e r f o r m -
examples of variables that have been investi- ance s t a b i l i t y (IMEP v a r i a t i o n s ) is understood
gated as functions of engine operating condi- in q u a n t i t a t i v e detail.

tions and, more rarely, of combustion chamber The v i e w taken in t h i s study i s t h a t the
geometry. Individual studies concentrated on combustion c h a r a c t e r i s t i c s , s p e c i f i c a l l y igni-
the variability of either the combustion or t i o n d e l a y and combustion d u r a t i o n (defined
the cylinder pressure development without
attempting to link the two. As a consequence a -Numbers i n brackets designate references at end
complete understanding of the effects of engine of paper.

ABSTRACT

Comprehensive single-cylinder engine data combustion, in turn, was affected by both the
for three combustion chambers were analyzed engine operating conditions and chamber geomet-
statistically in order to quantify the effects ric characteristics. The chemical factors --
of engine operating conditions and chamber air fuel ratio and residual fraction -- affected
geometric variables on c o m b u s t i o n characteris- both the length and variability of combustion
tics, and o f combustion on e n g i n e performance (on a crank angle basis). The physical
stability. Operating condition variables of factors chamber geometry, spark timing,
interest were air-fuel ratio, residual fraction engine speed, and fueling level -- affected
(internal plus external EGR), spark timing, primarily the length of the combustion event
engine speed, and fueling level (trapped fuel and secondarily the steadiness of combustion.
per cycle). Geometric parameters of importance Currently, the most practical approach for
were chamber "openness" and squish. improving engine stability appears to be
Combustion and e n g i n e performance stability shortening of the overall combustion event.
were found to be related such that engine Adjustments of physical factors, particularly
stability was improved when combustion varia- chamber openness and turbulence-generating
tions were reduced, as would be e x p e c t e d , and/or features, provide a good o p p o r t u n i t y for
when the combustion event was shortened. The achieving this reduction.

0148-7191/80/0225-0459S02.50
Copyright © 1980 Society of Automotive Engineers, Inc.
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2 800459

l a t e r ) , d i c t a t e the nature of the engine c o m b u s t i o n i s d e t e r m i n e d by e n g i n e o p e r a t i n g

performance (IMEP) v a r i a b i l i t y . The combustion c o n d i t i o n s and c h a r a c t e r i s t i c s o f t h e combustion
i s regarded o v e r a l l a s an i n t e r m e d i a t e phenome- c h a m b e r , d e p i c t e d by t h e b o x e s a t t h e l e f t o f
n o n w h i c h i s a f f e c t e d by b o t h e n g i n e o p e r a t i n g Fig. 1. Flow from causes to the f i n a l e f f e c t is
c o n d i t i o n s and combustion chamber g e o m e t r y , and from l e f t to r i g h t .
which, in turn a f f e c t s the s t a b i l i t y of engine Absent from the path diagram a r e v a r i a b l e s
performance. The r e s u 1 t s o f t h i s study include to represent e x p l i c i t l y in-cyHnder turbulence
q u a n t i t a t i v e r e l a t i o n s h i ps b e t w e e n c o m b u s t i o n and f l o w s , w h i c h a r e g e n e r a l l y a c c e p t e d t o be
c h a r a c t e r i s t i c s and engine performance the o r i g i n of c y l i c d i s p e r s i o n in engines
s t a b i l i t y , and a q u a n t i t a t i v e u n d e r s t a n d i n g of [H,15J. S u c h v a r i a b l e s c o u l d n o t be i n c l u d e d
the e f f e c t s of both engine operating c o n d i t i o n s rn t h e a n a l y s i s b e c a u s e i n - c y l i n d e r f l o w m e a s -
and c o m b u s t i o n chamber c h a r a c t e r i s t i c s on u r e m e n t s w e r e n o t made d u r i n g t h e e n g i n e t e s t s .
combustion. The scope o f t h i s work i s limited B e c a u s e no e f f o r t s w e r e made t o a l t e r a r t i f i -
t o c y c l i c v a r i a t i o n s o c c u r r i n g d u r i n g normal c i a l l y the c y l i n d e r f l o w s from what would
combustion in s i n g l e - c y l i n d e r e n g i n e s . Varia- n a t u r a l l y o c c u r due to chamber c o n f i g u r a t i o n ,
t i o n s due to abnormal c o m b u s t i o n , e . g . , m i s f i r e s , and because i n t a k e systems f o r a l l chambers were
d e t o n a t i o n , and i n c o m p l e t e c o m b u s t i o n , o r s i m i l a r , i t was assumed t h a t the g e o m e t r i c
c y l i n d e r - t o - c y ! i n d e r d i f f e r e n c e s in m u l t i - p a r a m e t e r s c o u l d be used to c h a r a c t e r i z e
cylinder engines are excluded. chamber-to-chamber d i f f e r e n c e s in geometry and
in-cylinder flows.

CAUSE-AND-EFFECT RELATIONSHIPS
DATA BASE
Analyses of the experimental data were
based on the overall cause~and-effeet relation- The data used in this study were obtained
ships shown in the path diagram of Fig. 1. from engine tests performed during a combustion
Statistical analysis was used to identify the chamber study [19] in which the performances of
important cause-effect paths and to quantify two c o m b u s t i o n chambers an open and a
their relative strengths. In Fig. 1, the boxes wedge -- w e r e compared. Additional data from
represent various physical quantities and engine tests of a modified wedge chamber [20]
phenomena. The a r r o w s indicate the cause-effect were also included. All engine builds had
paths -- the causes residing at the tails, and identical bores ( 9 5 mm) a n d strokes (88.4 mm).
the effects at the heads o f the arrows. Start- Cross-sections showing the shapes and spark plug
ing from the right of Fig. 1 , we s e e that engine locations of these three chambers are shown in
stability is directly affected by both combus- Fig. 2.
tion and spark timing. Spark timing, as it In t h e r e f e r e n c e d chamber s t u d y , single-
determines the phasing of combustion to cylinder c y l i n d e r engines were tested over ranges of
volume, impacts directly on e n g i n e stability. operating conditions. The t e s t - p o i n t m a t r i x f o r
Spark timing indirectly influences engine t h e e n g i n e t e s t s was based on a c o m p o s i t e
stability through its affect on combustion experimental design [19,23] in which wide ranges
(solid arrow from spark timing to combustion). o f o p e r a t i n g c o n d i t i o n s c o u l d be c o v e r e d w i t h a
At a more fundamental level, the nature of m o d e r a t e number o f t e s t p o i n t s . The o p e r a t i n g

CHAMBER

RESIDUAL
FRACTION

A I R - F U E L RATIO
WEDGE CHAMBER OPEN CHAMBER
ENGINE
STABILITY
ENGINE SPEED

FUELING LEVEL

S P A R K TIMING

MODIFIED W E D G E CHAMBER

Fig. 1 - Overall path diagram showing assumed

dependence of engine stability on c o m b u s t i o n and Fig. 2 - Cross-sections of combustion chambers
spark timing and of combustion on e n g i n e operat- investigated in this study. Note spark
ing conditions and chamber geometry locat ions
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800459 3

condition variables were a i r - f u e l ratio, this context, had the highest coefficient of
external exhaust gas recirculation (EGR), engine determination (R-square), which is a measure of
speed, spark timing, and fueling level. how w e l l the equation explains the variation of
Although external EGR w a s varied during the the data [23]. The "good" equations had lower
engine tests, trapped residua1 fraction R-square values. From this choice of equations,
(internal plus external EGR) was used as an t h e model equation with t h e optimum number and
explanatory (independent) variable in the most physically meaningful terms was selected.
analyses of the data. The ranges of the varia- RIDGE was used to search for significant
bles, along with average and standard devia- multi-col1inearity, i.e., high correlation
tions, are summarized in the tables and figures between explanatory variables, in the regression
of Appendix A. In total, 146 t e s t points were equation [22,25], and to modify the regression
included in the data base. In a d d i t i o n to coefficients (Bn's in Eq. 1) as necessary.
steady state data, 96 c o n s e c u t i v e cycles of Mu1ti-col1inear effects were found to be unim-
cylinder pressure data were recorded at each portant in this study.
test point. Test fuel was Indolene Clear. VARIABLES OF INTEREST - The explanatory
Detailed descriptions of the engine test points, and response variables considered in this study
test procedures, and engine characteristics can are shown in the path diagrams of engine
be found in Refs. 19 a n d 20. combustion (Fig. 3) and engine performance
stab!1ity (Fig. 4).
DATA ANALYSIS Engine Combustion Path Diagram - The
explanatory variables, shown a t the left of
In the composite-design based engine tests Fig. 3, were the chemical factors of air-fuel
[19], many o p e r a t i n g conditions were varied ratio and trapped residual gas fraction
simultaneously, confounding the effects of the (internal plus external EGR), and the physical
individual variables on both combustion and factors of spark timing, engine speed, fueling
engine performance. To separate the individual level, and two g e o m e t r i c parameters character-
effects, statistical procedures, namely regres- izing combustion chamber squish and openness.
sion analyses, were employed. In these statis- Two o t h e r parameters were used as candidate
tical analyses, equations were generated to geometric variables, but were not found to be
quantify the effects of the explanatory important (see Appendix B). The response varia-
(1ndependent) variables on the response (depend- bles, shown collectively at the right of Fig. 3,
ent) variables. The general form of a regres- consist of means and variations of both ignition
sion equation was: delay and combustion duration (defined later).
In addition to the main path diagram, two
RESPONSE = BO + B f TERM! + B2 TERM2 other path diagrams in which spark timing and
residual fraction are secondary response varia-
+ + Bn TERMn 0 ) bles are shown in Fig. 3 as broken lines. These
diagrams reflect the practical constraints
where RESPONSE is the dependent variable, Bn's placed on the highest permissible level of an
are the regression coefficients, and the TERMn's explanatory variable by the other explanatory
are the explanatory terms. Various statistical variables. The secondary paths connecting
software packages were used to select appropri- chamber geometry and air-fuel ratio to residuals
ate terms from c a n d i d a t e terms and to calculate illustrate that the maximum level of residuals
the corresponding regression coefficients. that can be tolerated by an engine under normal
STATISTICAL SOFTWARE PACKAGES - Three combustion is dependent on the chamber geometry
available software packages were used to analyze and air-fuel ratio. Similarly the secondary
these data: SPSS [22], SCREEN [23] and RIDGE path connecting chamber geometry, air-fuel
[24]. Although each of these packages supported ratio, residuals, engine speed, and fueling
regression analyses, each had u n i q u e features level to spark timing illustrates that the
which were utilized. maximum p r a c t i c a l spark advance, namely MBT, is
SPSS was used for the initial data analyses dependent on chamber geometry and engine operat-
to determine if geometric factors had noticeable ing conditions. In all engine tests levels of
effects on e n g i n e combustion. Through the use spark advance and residual fraction were
of dummy v a r i a b l e s [22] to represent the various within the acceptable limits.
chambers, the importance of chamber geometry was
detected without having to include detailed Engine Performance Stab 11ity Path Diagram -
geometric data. Where chamber geometry was Engine performance stability was assumed to be
found to be important, further regression analy- a response variable resulting directly from the
ses, which included detailed geometric factors combustion process and the phasing of the
as explanatory variables, were carried out. combustion to the cylinder volume, Fig. 4. The
SCREEN was used to provide a range of explanatory variables were the means and
acceptable equations -- a " b e s t " and several variations of ignition delay and combustion
"good" equations -- from which the final model duration, as they characterize the combustion
equation was chosen. The " b e s t " equation, in process, and spark timing, as it phases the
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800459
4

CHAMBER
GEOMETRY

RESIDUAL
FRACTION

COMBUSTION
• AIR-FUEL RATIO
MEANS & VARIATIONS
OF

IGNITION COMBUSTION
h-- ENGINE SPEED DELAY DURATION

FUELING LEVEL

- SPARK TIMING

F i g . 3 - Combustion path diagram: Primary paths

( s o l i d l i n e s ) a r e from o p e r a t i n g c o n d i t i o n s and
chamber geometry to c o m b u s t i o n . Secondary paths
(broken lines) i n d i c a t e t h a t maximum l e v e l s o f
r e s i d u a l f r a c t i o n and s p a r k t i m i n g a r e restrict-
e d by o t h e r variables

S P A R K TIMING Engine Operating Conditions - These varia-

bles were generally the simplest to determine.
Air-fuel ratio, engine speed, and spark timing
ENGINE
were obtained from d i r e c t measurements or from
PERFORMANCE
STABILITY calculations using steady-state measurements
made in the test cell. Similarly, fueling
COMBUSTION level, defined as the mass of fuel trapped per
M E A N S & VARIATIONS unit displacement per cycle, was also obtained
OF
from d i r e c t measurement. In contrast, a
IGNITION COMBUSTION sophisticated engine simulation program, similar
DELAY DURATION
to that described in Ref. 26, was used to
estimate the trapped cylinder residual gas
fraction (including external EGR) because
Fig. h - Engine stability path diagram showing direct experimental measurements of this quanti-
that combustion impacts directly on engine ty were not made.
stability, while spark timing affects both Chamber Geometry Parameters - Four
combustion and e n g i n e stability variables, intake valve area, squish area,
maximum f l a m e travel distance, and a chamber
openness parameter, were used to describe the
combustion chamber geometry (see Appendix 8).
combustion to the c y l i n d e r volume. Spark Only two o f these variables, squish area and a
t i m i n g a l s o had an i n d i r e c t e f f e c t t h r o u g h its chamber openness parameter, were found to be
i n f l u e n c e on the combustion p r o c e s s , as important. Squish, the percent of the total
described previously. bore area for which the clearance between the
Q U A N T I T A T I V E D E T E R M I N A T I O N OF V A R I A B L E S - piston and cylinder head at top dead center is
Many o f t h e e x p l a n a t o r y v a r i a b l e s r e q u i r e d f o r equal to the gasket thickness, was computed for
t h e a n a l y s i s o f t h e e n g i n e combustion and each chamber from measurements of piston-crown
p e r f o r m a n c e s t a b i l i t y r e s p o n s e d a t a can be and cylinder-head contours. The openness
measured d i r e c t l y i n t h e t e s t c e l l o r c a n be parameter is related to the accessibility of
computed s i m p l y from t e s t c e l l measurements. the combustion chamber volume to a spherical
O t h e r s , h o w e v e r , r e q u i r e more d e t a i l e d and flame propagating from the spark plug location,
s o p h i s t i c a t e d c a l c u l a t i o n s using heat release and is influenced by both the shape of the
a n a l y s i s and e n g i n e s i m u l a t i o n computer combustion chamber and the location of the
programs. spark plug. Values for the openness parameter
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800459 5

were computed by least-squares fitting of Wiebe

functions to curves of volume-burned fraction
versus normalized flame-radius (Fig. 5) that
were obtained from an a n a l y s i s of the combustion
chamber geometry at top dead center (see
Appendix B). Larger values of openness reflect
a more accessible combustion volume for a given
flame radius. Further detailed discussion of
the geometric parameters is given in Appendix B.
Engine Performance Stability Parameter -
Engine performance stability was characterized
by the variation in IMEP and was quantified by
the ratio of the standard deviation of IMEP to
the average IMEP computed for 96 consecutive
firing cycles. This ratio was multiplied by
100 t o express engine stability as a percentage.
IMEP w a s computed by integrating measured
cylinder pressure over the cylinder volume
during the compression and expansion strokes of F i g . 5 - Volume-burned f r a c t i o n (V/V_) versus
the engine cycle. normalized flame radius curves for the open,
Combustion Var?ables - A mass-burned wedge, and modified~wedge chambers a t top dead
f r a c t ion curve "(such " a s F i g . 6), which was center
inferred from heat release analysts on measured
cylinder pressure data, was used to characterize
engine combustion. Two p a r a m e t e r s were used to
describe this curve: ignition delay and
combustion duration. Ignition delay was defined
to be the crankangle interval between the time
of spark and a t t a i n m e n t of \% m a s s burned.
Combustion duration was defined to be the
crankangle interval between the }% and 90% m a s s -
burned points. Detailed thermodynamic [273 and
a more a p p r o x i m a t e [283 heat release analyses
were used to compute the values of the combus-
tion parameters f r o m 9& c o n s e c u t i v e pressure
cycles (see Appendix C). Averages and standard
d e v i a t i ons of both ignition delay and combustion
duration, computed from these 96 pressure
cycles, were used to characterize the mean
combustion and the cyclic combustion variabili- -60 -40 -20 0 20 40 60 80 100
ty, respectively. CRANK ANGLE

CANDIDATE TERMS IN REGRESSION EQUATION

ANALYSIS - In regression analyses the user has Fig. 6 - Mass-burned fraction curve showing
to specify the candidate explanatory (independ- ignition delay and combustion duration
ent) terms for possible inclusion in the
resultant regression equation. Only a few
terms are needed if the user knows exactly
which explanatory variables are important and terms, which show the effect of an explanatory
how e a c h affects the response variable, e.g., variable on the response variable in the
in a linear, quadratic, exponential manner. If presence of other explanatory variables, were
the user does not have this information, many also included as candidate terms. These terms
terms are needed, and the statistical analysis were limited to the 1inear-by-1inear combina-
is relied on to select the important explanatory tions of two v a r i a b l e s , e.e., products of two
variables. In this study, all previously explanatory variables. The contribution of the
described explanatory variables were included. higher order terms was assumed to be negligible.
Both linear and quadratic forms of all explana- Although many candidate terms were included
tory variables, except chamber openness, could in the statistical analyses of the combustion
be used to represent their main effects. Only data (34 w i t h geometry and 20 w i t h o u t geometry)
the linear chamber openness term was applicable and the engine stability data (20 terms), only
because the test values were concentrated at six or seven terms were required to obtain
end points of the range: ll.3 for the open, satisfactory regression equations. Addition of
and 5.6 and 6.2 for t h e wedge and modified- more terms to the regression equation did not
wedge chambers, respectively. Interaction result in an improved fit.
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6 800459

RANGE OF V A R I A B L E S AND R E S U L T A N T INFERENCE R-square

S P A C E S - An i m p o r t a n t c o n s i d e r a t i o n a l w a y s
r e l a t e d to s t a t i s t i c a l analyses of experimental Combust i o n
data is the inference space, i . e . , the ranges Durat ion with geometry without geometry
of values of the (explanatory) v a r i a b l e s for
which the r e s u l t a n t regression equation is Mean 0.86 0-53
valid. The i n f e r e n c e space i s intimately Variation 0.84 0.60
r e l a t e d to the range of the e x p l a n a t o r y varia-
bles s u r v e y e d , plus the combinations of ranges
T h e s e r e s u l t s , t o o , make s e n s e physically,
of these f a c t o r s . For example, although the
a s b o t h t h e shape o f t h e c o m b u s t i o n chamber and
ranges of a i r - f u e l r a t i o and r e s i d u a l fraction
the spark plug location determine the a c c e s s i -
e x t e n d e d f r o m 15 t o 19 a n d f r o m 0 . 1 0 t o 0.k\ t
b i l i t y of the fresh charge to the propagating
r e s p e c t i v e l y , t h e o c c u r r e n c e o f an a i r - f u e l
flame, i.e., t h e amount o f chamber v o l u m e
r a t i o o f 19 w i t h a r e s i d u a l f r a c t i o n o f 0.h\
w i t h i n a spherical flame centered at the spark
was not a v a l i d c o m b i n a t i o n , a s the e n g i n e
location. Squish turbulence is also influential
t e s t s d i d not i n c l u d e such d i l u t e c o n d i t i o n s ,
during t h i s combustion interval.
where e n g i n e o p e r a t i o n was u n s a t i s f a c t o r y . The
B e c a u s e MBT s p a r k t i m i n g r e f l e c t s the
ranges of e x p l a n a t o r y v a r i a b l e s of F i g s , 3 and
phasing of the combustion event to the c y l i n d e r
k a l o n g w i t h t h e i r means a n d s t a n d a r d d e v i a -
v o l u m e , MBT t i m i n g i s a l s o a f f e c t e d by t h e
}

t i o n s , a r e s u m m a r i z e d by t a b l e s a n d f i g u r e s in
chamber geometry, m a i n l y through t h e e f f e c t o f
Append ix A .
•geometry on c o m b u s t i o n d u r a t i o n . When t h e
dummy g e o m e t r i c v a r i a b l e s w e r e u s e d i n t h e
RESULTS OF DATA ANALYSES a n a l y s i s o f t h e MBT d a t a , R - s q u a r e increased
from 0.81 to 0.89.
The r e s u l t s o f the s t a t i s t i c a l a n a l y s e s of QUANTITATIVE RESULTS - Q u a n t i t a t i v e results
the e x p e r i m e n t a l combustion and engine stability of the s t a t i s t i c a l analyses are presented in
data are presented below. R e s u l t s of the three forms: ( 1 ) t h e s e l e c t e d model regression
i n i t i a l analyses to determine q u a l i t a t i v e equation of a form corresponding to Eq. 1 ,
e f f e c t s o f chamber geometry on t h e c o m b u s t i o n together w i t h s t a t i s t i c a l data summarizing both
are presented f i r s t . R e s u l t s o f t h e more the regression "goodness" of f i t ( R - s q u a r e ) and
d e t a i l e d a n a l y s e s , including the q u a n t i t a t i v e the a v e r a g e d i f f e r e n c e between the p r e d i c t i o n s
e f f e c t s o f t h e chamber g e o m e t r y , follow. o f the r e g r e s s i o n e q u a t i o n and t h e measured
Q U A L I T A T I V E I N F L U E N C E OF CHAMBER GEOMETRY d a t a (RMS e r r o r ) ; ( 2 ) t a b u l a r s u m m a r i e s o f the
ON C O M B U S T I O N - T h e i n i t i a l a n a l y s e s o f t h e q u a l i t a t i v e e f f e c t of each explanatory variable
combustion data were aimed a t e s t a b l i s h i n g the on t h e r e s p o n s e v a r i a b l e s ; and ( 3 ) c a r p e t plots
i m p o r t a n c e of t h e chamber geometry on the showing the o v e r a l l q u a n t i t a t i v e e f f e c t s o f the
c o m b u s t i o n t h r o u g h t h e u s e o f dummy v a r i a b l e s e x p l a n a t o r y v a r i a b l e s on t h e r e s p o n s e v a r i a b l e s .
[22]. In u s i n g t h e s e r e s u l t s , t h e r e a d e r i s c a u t i o n e d
t o keep in mind t h e i n f e r e n c e spaces f o r w h i c h
B o t h mean a n d v a r i a t i o n s o f i g n i t i o n d e l a y
the r e s u l t s a r e v a l i d (see Appendix A ) .
w e r e f o u n d t o be v e r y i n s e n s i t i v e t o t h e d e t a i l s
o f t h e chamber g e o m e t r y . C o e f f i c i e n t s of E f f e c t s o f Combustion on E n g i n e S t a b i J J t y -
determination ("goodness" of f i t , or R-square) E q . 2 i s t h e model r e g r e s s i o n e q u a t i o n s h o w i n g
f o r r e g r e s s i o n s w i t h a n d w i t h o u t t h e dummy t h e e f f e c t s o f t h e c o m b u s t i o n v a r i a b l e s and
v a r i a b l e s w e r e n o t v e r y d i f f e r e n t , a s shown a b s o l u t e s p a r k t i m i n g on n o r m a l i z e d IMEP v a r i a -
b e 1ow. tions. R - s q u a r e a n d RMS e r r o r v a l u e s a s s o c i a t e d
R-square w i t h t h i s e q u a t i o n were 0.97 ( r e l a t i v e t o a
maximum v a l u e o f 1 . 0 ) a n d 0.6%, respectively.
ignition Delay with geometry without geometry The s y m b o l i c v a r i a b l e names in E q . 2 a r e d e f i n e d
in Table 1 . Corresponding carpet plots are
Mean 0.95 0-94 shown in F i g s . 7 t h r o u g h 10.
Variation 0.80 0-78

These results make sense physically, as the

developing flame kernel is small and in all
chambers its growth is influenced by o n l y the
Table 1 - Q u a l i t a t i v e E f f e c t s o f V a r i a b l e s on Engine StabMity
wall in which the spark plug is located.
Additionally, this combustion period occurs IMEP
Increase Variation Reason
before piston top dead center, when squish
turbulence is minimal. Combustion D u r a t i o n (DUR) 1 ncreases Worsens p-v phasing
1gni t i o n Delay ( 0 £ L ) 1 ncreases Worsens p-v phasing
In contrast, combustion duration was V a r i a t i o n of Combustion Increases I n c r e a s e s v a r i a t i o n in
highly dependent on the chamber geometry, as D u r a t i o n (DOUR) p-v phasing
V a r i a t i o n of I g n i t i o n Increases
indicated by the large differences in R-square I n c r e a s e s v a r i a t i o n in
Delay (DDEL) p-v phasing
with and w i t h o u t the dummy g e o m e t r i c variables Spark Advance (SPK) Decreases Improves p-v phasing
in the reg ress i o n s . (toward MBT)
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800459

IMEP Var - - ,03128 - . 4 8 9 1 1 DOUR in conjunction with spark timing determine the
strength of the coupling between combustion and
+ .63027E-O3 DUR DUR + ,011254 DDEL engine stability. This is accomplished by the
phasing of the combustion and subsequent
* .10302 DOUR D D E L - .022400 SPK DDEL cylinder pressure to the cylinder volume (p~v
phasing in Table l ) . Improved phasing, corres-
+ .72527 DDUR DEL/SPK (2) ponding to more energy release at piston
positions around top dead center, attenuates
Although the results presented in Eq. 2 the coupling between the combustion variability
and in Figs. 7 through 10 w e r e determined from and engine stability. At a more fundamental
engine tests of open, wedge, a n d mod I f t e d - w e d g e 1eve 1, a reduction of the combustion variations
combustion chambers, they are generally applica- results In decreased IMEP variations (improved
ble to other chamber configurations having the engine performance stability).
same ranges of combustion variables and spark From t h e s e results, several general conclu-
timing, i.e., the same inference space (Tables sions can be reached with regard to maximizing
A-2 and A~3> A p p e n d i x A). eng i ne stab11i ty ( m J n i r c i z i ng I HEP v a r i a t i o n s ) ,
Qualitative effects of increasing each At fixed spark timing, maximum e n g i n e stability
explanatory variable, one at a time, on IMEP occurs with the fastest (shortest Ignition
variations and the reasons for these effects delay and combustion duration) and steadiest
are summarized in Table 1- The lengths of the
ignition-delay and combustion-duration interval;
10
DURATION VAR,
DURATION VAR. 9.0 C A D E G .
6.0 C A D E G
5.5
DURATION VAR. DURATION VAR.
§ 5 4.0 C A D E G 6.0 CA D E G A

U4.5
DURATION VAR.
£ 4 " 2 0 CA DEG ^ >
$ 5 Q

- D E L A Y V A R . - 1.0 C A D E G D E L A Y V A R . - 1.5 CA D E G
D E L A Y V A R . - 2,0 C A D E G D E L A Y V A R . - 3.0 C A D E G

Fig. 7 - Engine stability (IMEP variation) Fig. 8 - Engh f s t a b i l i t y (IMEP variation)

carpet plot spark timing = 15 carpet plot -• spark timing = 25 BTDC

20 r
DURATION VAR.
12.0 C A D E G , „ t 8 DURATION VAR.
15.0 C A D E G •
b~
DURATION VAR.
L> 10.0 C A D E G
us * H

a.
z 1 2 DURATIOr
5.0 C A D E G . V
§10 Lit

1
cc 8
<
> 6
a
UJ ^

0
- DELAY VAR. - 2 0 CA DEG D E L A Y V A R . - 2.5 CA D E G
D E L A Y V A R . - 4.0 C A D E G D E L A Y V A R . - 5.0 C A D E G

Fig. 9 - Engine stability (IMEP variation) Fig. 10 - E n g i n e stability (IMEP variation)

carpet plot -- spark timing - 35 BTDC carpet plot -- spark timing = 45 BTDC
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8 800459

( l o w e s t v a r i a t i o n s o f d e l a y and d u r a t i o n ) d e f i n i t i o n s , t h e p r i m a r y and s e c o n d a r y classifi-

combustion. This c o n d i t i o n corresponds to the c a t i o n s apply only w i t h i n the range of the data
l o w e s t , l e f t - m o s t p o i n t in F i g s . 7 t h r o u g h 10. tested.
W i t h f i x e d c o m b u s t i o n c h a r a c t e r i s t i c s , more T h e mean i g n i t i o n d e l a y w a s a f f e c t e d by
a d v a n c e d s p a r k t i m i n g s ( n o t e x c e e d i n g MBT a l l f i v e o p e r a t i n g c o n d i t i o n s , a s shown by E q .
timing) improve e n g i n e performance stability 3. T h e r e g r e s s i o n - a s s o c i a t e d R ~ s q u a r e a n d RMS
(compare s i m i l a r p o i n t s from f i g u r e to f i g u r e ) . e r r o r were 0.94 and f . 8 c r a n k a n g l e (CA) d e g r e e s ,
A d d i t i o n a l l y , the c a u s a l p a t h s from the respectively. A corresponding carpet plot is
combustion and s p a r k - t i m i n g v a r i a b l e s t o t h e shown i n F i g . 1 1 . The s e n s i t i v i t y of ignition
e n g i n e s t a b i l i t y v a r i a b l e , and t h e relative d e l a y to e n g i n e speed changes i s i n d i c a t e d in
p a t h s t r e n g t h s , c a n be d e t e r m i n e d . The r e l a t i v e the figure caption.
s t r e n g t h o f e a c h c a u s a l p a t h , i . e . , t h e amount
o f change in e n g i n e s t a b i l i t y in response to DEL - -1.97 + .0047106 SPK SPK + .025702 AF AF
c h a n g e s i n e a c h e x p l a n a t o r y v a r i a b l e , c a n be
i n f e r r e d from F i g s . 7 t h r o u g h 10. Such informa- + .08784 FL RPM - 9 1 7 - 6 6 7 FL RES
t i o n i s v a l u a b l e i n m a k i n g t r a d e - o f f s among
c o m b u s t i o n , s p a r k t i m i n g , and e n g i n e stability,
+ 76.844 RES RES + 2.3857 AF RES (3)
o r in making c o s t - b e n e f i t e v a l u a t i o n s to
d e t e r m i n e , f o r e x a m p l e , the most e f f i c i e n t
The qualitative main effects of individual
method f o r i m p r o v i n g e n g i n e p e r f o r m a n c e
increases of the operating conditions on.the
stab i!i ty.
mean ignition delay (and for ignition delay
A t a more f u n d a m e n t a l l e v e l , h o w e v e r , t h e variations, discussed later) are listed in
c o m b u s t i o n i s a n i n t e r m e d i a t e phenomenon w h i c h Table 2. Probable reasons for these effects
i s a f f e c t e d by t h e e n g i n e o p e r a t i n g c o n d i t o n s are discussed later in the DISCUSSION OF
and chamber g e o m e t r y a n d , in t u r n , affects RESULTS. Overall, minimum ignition delay
engine s t a b i l i t y (Fig. 1). In t h e f o l l o w i n g occurred at conditions of lowest residual
s e c t i o n s , the causal paths l i n k i n g the engine fraction, least lean air-fuel ratio, most
o p e r a t i n g c o n d i t i o n s and combustion chamber retarded spark timing, highest fueling level,
geometry to the engine combustion c h a r a c t e r i s -
t i c s , and t h e r e l a t i v e s t r e n g t h s o f these
p a t h s , a r e e v a l u a t e d f o r t h e o p e n , wedge, and
S P A R K ADV.
modified-wedge combustion chambers. From t h e s e
60.0 C A D E G . .
d e r i v e d r e l a t i o n s h i p s among o p e r a t i n g c o n d i -
t i o n s , chamber g e o m e t r y , and c o m b u s t i o n , and
"•<>.<
between c o m b u s t i o n and e n g i n e s t a b i l i t y (Figs.
7 through 1 0 ) , the paths from the fundamental
e n g i n e o p e r a t i n g c o n d i t i o n s and chamber geometry
t o t h e c o m b u s t i o n , and then t o t h e e n g i n e
stability characteristics are established for
the chambers c o n s i d e r e d in t h i s study.

E f f e c t s o f O p e r a t i n g C o n d i t i o n s and
Chamber G e o m e t r y on C o m b u s t i o n - In a d d i t i o n t o F U E L I N G L E V E L - 0.024 G / L / C Y C L E
presenting the r e s u l t s of the analyses of the F U E L I N G L E V E L - 0.038 G / L / C Y C L E
combustion d a t a in e q u a t i o n , t a b u l a r , and
graphical forms, the strength of each cause-
e f f e c t p a t h was e x p l o r e d , and e a c h e x p l a n a t o r y
v a r i a b l e was c l a s s i f i e d e i t h e r a s p r i m a r y o r Fig. 11 - Ignition delay carpet plot -- engine
s e c o n d a r y , d e p e n d i n g upon t h e s t r e n g t h o f its s p e e d = 1700 r/min. Ignition delays at other
e f f e c t on t h e r e s p o n s e v a r i a b l e . Determination engine speeds can be determined by adding
o f t h e s t r e n g t h o f a g i v e n r e l a t i o n s h i p was A DELAY from the equation below to the value
made by e v a l u a t i n g t h e r e g r e s s i o n e q u a t i o n w i t h of the ignition delay from the plot.
the explanatory v a r i a b l e of i n t e r e s t set at low
A DELAY = 0 . 0 8 7 8 4 FL [RPM - 1700.];
and a t h i g h v a l u e s c o r r e s p o n d i n g t o one s t a n d a r d
FL = f u e l t ng 1evel
d e v i a t i o n b e l o w a n d a b o v e t h e mean v a l u e ,
r e s p e c t i v e l y , while keeping the remaining
e x p l a n a t o r y v a r i a b l e s a t t h e i r mean v a l u e s (see
A p p e n d i x A f o r means and s t a n d a r d d e v i a t i o n s ) . T a b l e 2 - Q u a l i t a t i v e E f f e c t s of Operating
C o n d i t i o n s on i g n i t i o n Delay
I f t h e r e s u l t i n g change in r e s p o n s e were
n o t i c e a b l y l a r g e r t h a n t h e r e g r e s s i o n RMS I ncrease I g n i t i o n D ei ay i Delay V a r i a t ions
e r r o r , t h e v a r i a b l e c a u s i n g t h a t c h a n g e was>
Residuals (RES) Increases Increases
d e f i n e d t o be a p r i m a r y e x p l a n a t o r y v a r i a b l e .
A i r - f u e l R a t i o (AF) Increases Increases
O t h e r w i s e i t w a s d e f i n e d t o be a s e c o n d a r y Spark Advance (SPK) Increases Increases
variable. B e c a u s e o f t h e s e p r o c e d u r e s and Engine Speed (RPM) Increases I ncreases
Fueling Leve! (FL) Decreases Decreases
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800459 9

and lowest engine speed, Fig. 11. Evaluation of ignition delay occurred at conditions
of the relative strengths of the causal paths, corresponding to the shortest mean ignition
via the regression equation, revealed that delay, namely, the most retarded spark timing,
residual fraction, air-fuel ratio, and spark the 1owest residua1 fraction, the 1east 1ean
timing were primary explanatory variables, air-fuel ratio, the highest fueling level, and
whereas fueling level and engine speed were the lowest engine speed, Fig. 12. In contrast
secondary explanatory variables. Ignition to the mean ignition delay, however, only
delay increased by 7-7> 5 * 1 , and 6,2 CA degrees residual fraction and a i r - f u e l ratio appeared
in response to the low-to~high changes of the to be primary variables, with spark timing,
residual fraction, air-fuel ratio, and spark fueling level and engine speed being secondary
advance variables, respectively. In response variables. Again, evaluation of the regression
to the low-to-high changes of the fueling level equation, Eq. 4, with each explanatory variable
and engine speed variables, ignition delay at its low and high values, and the others at
increased by -0.8 and 1.2 CA d e g r e e s , respec- their mean v a l u e s , showed ignition delay varia-
tively. For comparison, the regression RMS tions increasing by 1.5 and 0.9 CA d e g r e e s when
error was 1.8 CA degrees. residual fraction and air-fuel ratio, respec-
Cycle-to-cycle variations of ignition tively, were increased. In response to the
delay were similarly affected by the five changes in spark timing, fueling level, and
operating conditions, as shown in Eq. 4. R- engine speed, ignition delay variations
square and RMS e r r o r values were 0.78 and 0.5 increased by only 0.6, - 0 . 5 , and 0.5 CA degrees,
CA d e g r e e s , respectively. A corresponding respectively. The regression RMS e r r o r for
carpet plot is shown in Fig. 12. The sensiti- these data was 0.5 CA degrees.
vity of the variation of ignition delay to In addition to being affected by the
engine speed changes is indicated in the engine operating conditions, the mean combus-
figure caption. tion duration was also strongly influenced by
the geometric squish and o p e n n e s s parameters.
DDEL = .32 + \397**9E-03 SPK SPK - 114-92 FL For the selected model regression equation, Eq.
5, R-square and RMS error were 0.83 and 6.0 CA
+ .094991 FL RPM ~ 3 8 9 . 8 5 FL RES degrees, respect ively. In Eq. 5, SPK! repre-
sents spark advance normalized by MBT timing.
- •53591E-06 RPM RPM Combustion duration carpet plots are shown in
Figs. 13, 14, and 15 f o r the open, wedge, and
+ 1.2683 AF RES (4) modified-wedge chambers, respectively. The
sensitivity of combustion duration to engine
Qualitatively, the ignition delay varia- speed changes is indicated in the figure
tions were affected by the operating variables captions. The effect of chamber geometry is
in the same m a n n e r as was the mean ignition
delay, Table 2. In general, minimum variations

_130
S P A R K ADV. O120
60.0 C A D E G
LU
SPK ADV/MBT SPK
<=» 110 0,50 SPK ADV/MBT SPK
A

0100 0.67, S P K A D V / M B T S P K
§ 9 0 0.84
19.0
b so I
18.0
< U J O

fi7.oG?j~
z 6 0
16.0
2 50

I 3 0
O
g 20 V ,
o
' ^ 0 ^ £ * V ~ - F U E L I N G L E V E L - 0.024 Q / L / C Y C L E
0
10
^ - - - F U E L I N G L E V E L - 0.038 G / L / C Y C L E o
— F U E L I N G L E V E L 0.024 G / L / C Y C L E x

- F U E L I N G L E V E L - 0.038 G / L / C Y C L E

Fig. 12 - Ignition-delay variation carpet

plot — engine speed - 1700 r/min. Variations Fig. 13 - O p e n - c h a m b e r combustion-duration
at other engine speeds can be d e t e r m i n e d by carpet plot — engine speed = 1700 r/min.
adding AVAR from the equation below to the value Durations at other engine speeds can be deter-
of variation from the plot. AVAR = [0.094991 mined by a d d i n g ADUR from the equation below to
FL • 0.53591E-06 [3400 + ARPM]] ARPM; ARPM = the value of duration from the plot. ADUR =
RPM - 1700 0.36958 FL [RPM - 1700.]; FL = fueling level
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10 800459

140r SPK ADV/MBT SPK _130

0.50 SPK ADV/MBT SPK <£>120
SPK ADV/MBT SPK
0.67 „ S P K A D V / M B T S P K
^110 0.50 SPK ADV/MBT SPK
0.84 SPK ADV/MBT SPK
y.100 i9.o 0.67
0.84

i 9 0

5 80
§ 70
- 6 0
g 50
3 4 0

| 30

8 2 0

F U E L I N G L E V E L - 0.024 G / L / C Y C L E 10 F U E L I N G L E V E L - 0.024 G / L / C Y C L E
F U E L I N G L E V E L - 0.038 G / L / C Y C L E F U E L I N G L E V E L - 0.038 G / L / C Y C L E

Fig. \k - Wedge-chamber combustion-duration F i g . 15 - M o d i f i e d - w e d g e c h a m b e r c o m b u s t i o n -

carpet plot -- e n g i n e s p e e d = 1700 r/min. d u r a t i o n c a r p e t p l o t — e n g i n e s p e e d - 3700
Durations at other engine speeds can be deter- r/min. D u r a t i o n s a t o t h e r e n g i n e s p e e d s c a n be
mined by a d d i n g ADUR f r o m the equation below to d e t e r m i n e d b y a d d i n g ADUR f r o m t h e e q u a t i o n
the value of duration from the plot. ADUR » below to the v a l u e o f d u r a t i o n from the p l o t .
0.36958 FL [RPM - 1700.]; FL = fueling level ADUR = 0 . 3 6 9 5 8 FL [RPM - 1 7 0 0 . ] ; FL = f u e l i n g
level

140

Table 3 Q u a l i t a t i v e E f f e c t s o f O p e r a t i n g C o n d i t i o n s and
Geometric V a r i a b l e s on Combustion D u r a t i o n

; 1 9 0
_j Combustion Duration
/1 a . o ^ p OPENNESS =12.0 Increase Duration Variation
, '17.0 U.h-
;

If'Me.o So? Residuals (RES) Increases I ncreases

;!5.0 < A i r - f u e l R a t i o (AF) increases I ncreases
Spark Advance ( S P K I ) Decreases Decreases
MBT t i m i n g
E n g i n e Speed (RPM) Increases \ncreases
Fueling Level (FL) Unchanged Decreases
Openness F a c t o r (OP) Decreases Decreases
S q u i s h (SQ) Decreases Increases

SQUISH
SQUISH

o p e r a t i n g c o n d i t i o n and chamber geometry v a r i a -

b l e o n t h e mean c o m b u s t i o n d u r a t i o n (and
Fig. 16 - E f f e c t s of chamber openness and v a r i a t i o n s of combustion d u r a t i o n , discussed
squish, residual fraction, and a i r - f u e l ratio on l a t e r ) a r e s u m m a r i z e d i n T a b l e 3- Qualitatively,
combustion duration spark/MBT - 0.67, engine f o r a g i v e n chamber c o n f i g u r a t i o n , F i g . 13, 14,
speed = 1700 r/min, fueling level = 0.031 o r 1 5 , minimum c o m b u s t i o n d u r a t i o n w a s o b t a i n e d
g/L/cycle w i t h minimum c h a r g e d i l u t i o n and most a d v a n c e d
s p a r k t i m i n g , a s s h o w n by t h e l o w e s t p o i n t in
t h e r i g h t - m o s t s e t o f maps i n e a c h f i g u r e .
Lower e n g i n e speed was a l s o c o n d u c i v e t o
shown in Fig. 16 f o r SPKI, engine speed, and shortening combustion d u r a t i o n . Fueling level
fueling level of 0.67, 1700 r/min, and 0.031 appeared to have a n e g l i g i b l e e f f e c t . For any
g/L/cycle, respectively. g i v e n e n g i n e o p e r a t i n g c o n d i t i o n , minimum
c o m b u s t i o n d u r a t i o n o c c u r r e d w i t h t h e most o p e n
c h a m b e r a n d maximum s q u i s h , a s s h o w n b y t h e
DUR = 2 0 . 6 0 + 2 0 . 3 8 4 A F RES + .36958 FL RPM
l o w e s t p o i n t i n t h e r i g h t - m o s t s e t o f maps i n
F i g . 16.
- 2788.6 FL RES -3-5553 RES SQ
Q u a n t i t a t i v e l y , the primary v a r i a b l e s
- 9-5132 R E S OP - 3 . 3 5 8 7 SPK! OP (5) a f f e c t i n g combustion d u r a t i o n , deduced from the
regression equation, were residual fraction,
For the above results, the qualitative air-fuel r a t i o , spark timing ( r e l a t i v e to MBT),
effects of increasing the value of each engine and b o t h chamber o p e n n e s s and s q u i s h . Secondary
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800459 11

explanatory variables were engine speed and The qualitative effects of increasing
fueling level. increasing each primary explana- engine operating conditions and chamber geometry
tory variable, one at a time, from its low to variables on the v a r i a t i o n of combustion dura-
high value resulted in increases of combustion tion are listed in Table 3- For a given
duration of 25-5 (residual fraction), chamber, Figs. 17, 18, or 1 9 , m i n imum c o m b u s -
(air-fuel ratio), -8.8 (spark advance/MBT tion duration variations occurred at conditions
timing), -10.7 (squish), and -21.5 (openness) of shortest combustion duration, namely, least
CA d e g r e e s . The c o r r e s p o n d i n g effect of changes lean air-fuel ratio, lowest residual fraction,
In the engine speed was o n l y a 5-2 CA degree highest fueling level, maximum s p a r k advance
increase in duration. The changes in fueling (relative to MBT), and lowest engine speed. At
level had a negligible effect, only a 0.3 CA a given operating condition, greater openness,
degree increase, on c o m b u s t i o n duration. For
compar i s o n , the regress ion-associated RMS error
was 6.0 CA degrees. 30
SPK ADV/MBT SPK S P K ADV/MBT SPK
The cyclic variation of combustion duration 050 SPK ADV/MBT SPK 0.84
was affected by all the engine operating condi-
UJ
I'9-0 0.67
tions and chamber geometry parameters, as shown Q 'J19.0

by Eq. 6. The a s s o c i a t e d R-square and RMS

3 2 0

error values were 0.85 and 1.6 CA degrees,

respectively. Corresponding carpet plots are O 15
shown in Figs. 17, 18, and 19 f o r the open, h- 10
<
wedge, and modified-wedge chambers, CC
respectively. The sensitivity of combustion
< Q
>
z
duration to engine speed changes is indicated o
in the figure captions. The e f f e c t of chamber
<
geometry is shown in Fig. 20 f o r SPKI, engine cc -5
speed, and fueling level of 0.67, 1700 r/min, 3
Q F U E L I N G L E V E L - 0.024 G / L / C Y C L E
and 0-31 g/L/cycle, respectively. -10 F U E L I N G L E V E L - 0.038 G / L / C Y C L E

DDUR - 2.38 - 99-311 RES + .1535^E-03 AF RPM

Fig. 18 - W e d g e - c h a m b e r combustion-duration
+ 8.1887 AF RES - .039136 AF OP variation carpet plot -- e n g i n e speed = 1700
r/min. Variations at other engine speeds can be
+ . 0 0 3 5 7 1 2 A F S0_ determined by adding ADDUR from the equation
below to the value of variation from the plot.
- 131 . M l FL SPKI (6) ADDUR = 0 . 1 5 3 5 ^ - 0 3 AF [RPM - 1700.];
AF - air-fuel ratio

30 r S P K A D V / M B T S P K
SPK ADV/MBT SPK SPK ADV/MBT SPK
SPK ADV/MBT SPK 0.67 0.50 S P K A D V / M B T S P K 0.84
£25
SPK ADV/MBT SPK f 19.0 0.67
0.50 A 19.0 Q
0.84
320 118.0;

i 1 5

< 10
cc
q <
>
z u

O o O
O 5 0 O

F U E L I N G L E V E L - 0.024 G / L / C Y C L E cc F U E L I N G L E V E L - 0.024 G / L / C Y C L E
F U E L I N G L E V E L - 0.038 G / L / C Y C L E F U E L I N G L E V E L - 0.038 G / L / C Y C L E

-10
Fig. 17 -
Open-chamber combustion-duration Fig. 19 -
Modified-wedge chamber combustion-
variation carpet plot engine speed = 1700 duration variation carpet plot -- e n g i n e speed =
r/min. Variations at other'engine speeds can be 1700 r/min. Variations at other engine speeds
determined by adding ADDUR f r o m the equation can be d e t e r m i n e d by adding ADDUR f r o m the
below to the value of variation from the plot. equation below to the value of variation from
ADDUR = 0 . 1 5 3 5 ^ - 0 3 AF [RPM - 1700.]; AF = the plot. ADDUR = 0 . 1 5 3 5 A E - 0 3 AF [RPM -
a i r-fuel r a t io 1700.]; AF = a i r - f u e l ratio
 Downloaded from SAE International by University of New South Wales, Sunday, August 19, 2018

12 800459

30 100r

525 O P E N N E S S ^6.0 .
ill 1900.0 R / M I N
,->p9 0 O P E N N E S S = 12.0
a 19.0
< 20 IJ 9.0
18.0 U J Q

15 17-0 O T P

10 ,'5.0 <

EE

-SQUISH - 0.0%
-10 - SQUISH = 16.0% F U E L I N G L E V E L - 0.024 G / L / C Y C L E
F U E L I N G L E V E L - 0.038 G / L / C Y C L E

Fig. 20 - E f f e c t s of chamber openness and

squish, residual fraction, and a i r - f u e l ratio on
combustion-duration variation -- spark/MBT = Fig. 21 Open-chamber MBT s p a r k timing carpet
0.67, engine speed - 1700 r/min, fueling level = plot
0.03! g/L/cycle

100 To u t i l i z e t h e model r e g r e s s i o n e q u a t i o n s
1900.0 R / M I N and t h e c o r r e s p o n d i n g c a r p e t p l o t s involving
n o r m a l i z e d s p a r k t i m i n g , t h e d e p e n d e n c e o f MBT
t i m i n g on e n g i n e o p e r a t i n g c o n d i t i o n s and
c h a m b e r c o n f i g u r a t i o n m u s t be known i n o r d e r t o
determine the acceptable absolute spark advances
( g r e a t e r o r e q u a l t o O.38 MBT, but l e s s t h a n
MBT i n F i g s . A - 4 a n d A - 5 , A p p e n d i x A ) a s
functions of operating conditions. MBT v a l u e s
f o r the t h r e e chambers were regressed a g a i n s t
t h e o p e r a t i n g c o n d i t i o n s and chamber geometry
variables. F o r t h e s e l e c t e d model e q u a t i o n ,
E q . 7 , R - s q u a r e a n d RMS e r r o r v a l u e s w e r e 0 . 8 9
a n d 4 . 0 CA d e g r e e s , respectively.
• F U E L I N G L E V E L - 0.024 G / L / C Y C L E
F U E L I N G L E V E L - 0.038 G / L / C Y C L E
0 L

MBT - -14.75 + .001315 AF RPM + .04362 AF AF

+ 5.518 AF RES + 976.1 FL RES

Fig. 22 - W e d g e - c h a m b e r MBT spark timing carpet
plot - .001033 RPM OP -17-93 FL SQ (7)

Figs. 2 1 , 2 2 , and 23 a r e corresponding

carpet plots for the open, wedge, and modified-
but l o w e r s q u i s h was c o n d u c i v e t o l o w e r varia- wedge c h a m b e r s , respectively. Fig. 24 is a
t i o n s of combustion d u r a t i o n , F i g . 20. carpet plot showing the effect of chamber
Quantitatively, the primary explanatory geometry o n MBT spark timing.
v a r i a b l e s were residual f r a c t i o n , air-fuel
r a t i o , and chamber o p e n n e s s . Secondary explana- AN A P P L I C A T I O N O F THE RESULTS
t o r y v a r i a b l e s w e r e chamber s q u i s h , fueling
l e v e l , e n g i n e s p e e d , and s p a r k t i m i n g . in As defined, the openness parameter includes
c o m p a r i s o n t o t h e r e g r e s s i o n RMS e r r o r o f 1.6 the e f f e c t s of both chamber shape and spark
CA d e g r e s s , i n c r e a s e s I n c o m b u s t i o n d u r a t i o n plug location. To separate the e f f e c t s of
v a r i a t i o n s o f 6 . 5 , 5-8 a n d - 3 . 3 CA d e g r e e s these two factors, combustion and engine
r e s u 3 ted from i n c r e a s i n g , In t u r n , res idua1 performance stability characteristics of four
f r a c t i o n , a i r - f u e l r a t i o , and chamber o p e n n e s s chambers, two a c t u a l and two hypothetical, were
v a r i a b l e s , r e s p e c t i v e l y , f r o m t h e i r low t o h i g h estimated using the previously described
values. S m a l l e r i n c r e a s e s of - 1 . 4 , - 1 . 2 , 1.2,
results. Actual chambers were the open and
a n d 0 . 8 CA d e g r e e s r e s u l t e d f r o m t h e l o w - t o -
wedge c h a m b e r s . Hypothet ica1 conf igurations
high changes of spark t i m i n g , f u e l i n g level,
were an open shape w i t h wedge-chamber spark
e n g i n e s p e e d , and chamber s q u i s h v a r i a b l e s ,
location (designated 0-WS, open-wedge spark)
respect ively.
and a wedge shape with open-chamber spark
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800459 13

100 100

O90
1900.0 R / M I N
80 1700.0 R / M I N 1 9 0
i
< A
18.0 O P E N N E S S = 12.0
'7.0 IX. P

z 60
< WJ16.0 9=jr
>
50
<

S I 40
cc
g 30
(f)
h- 2 0
CQ
S 10 F U E L I N G L E V E L - 0.024 G / L / C Y C L E
F U E L I N G L E V E L - 0.038 G / L / C Y C L E

S Q U I S H = 0.0%
- S Q U I S H = 16.0%
Fig. 23 - Mod i f i e d - w e d g e chamber MBT spark
timing carpet plot
Fig. 24 - E f f e c t s of chamber openness and
squish, residual fraction, and air-fuel ratio on
MBT spark timing engine speed » 1700 r/min.

estimates of combustion and e n g i n e performance

stability for these chambers can probably be
obtained from the regression equations and
carpet plots described earlier.
• ~ WEDGE CHAM. Quantitative estimates of the combustion
o = OPEN CHAM.— and e n g i n e stability behaviors of the 0-WS and
A = w—OS CHAM. W-OS c h a m b e r s can be o b t a i n e d graphically from
+ = O—WS CHAM. the carpet plots of Figs. 7 through 24, or by
computation using Eqs. 2 through 7. The
equations were used to estimate behaviors of
these chambers over a range of spark timings
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f r o m 0-38 MBT to MBT (consistent with the range
R / R
bore dia. shown in Fig. A-4 and A~5)- Combustion and
engine stability characteristics were also
computed for both t h e open and wedge chambers.
Fig. 25 - V o l u m e - b u r n e d fraction profiles Computed combustion characteristics of the
four chambers are shown in Figs. 26 t h r o u g h 29.
Ignition delays and delay variations, which
were previously found to be independent of
location (designated W-OS, wedge-open spark). chamber geometry for the chambers considered,
By comparing appropriately the behavior of are shown in Figs. 26 and 27. Limits on spark
these four chambers, the e f f e c t s of 1) altering advance for the chambers are indicated in all
spark location with fixed chamber shape, and 2) figures by vertical lines intersecting the
varying chamber shape w i t h fixed spark location curves. Labels, "0", "0-WS", "W", and "W-OS",
can be estimated. All comparisons were made at are used where necessary to identify the open,
air-fuel ratio, fueling level, engine speed, 0-WS, wedge, a n d W-OS c h a m b e r s , respectively.
and residual fraction of 17.3, 0.031 g/L/cycle, Combustion durations and duration variations
1700 r/min, and 0.22, respectively. are shown in Figs. 28 a n d 2 9 . The separate
Volume-burned fraction versus normalized effects of spark location and chamber shape can
flame radius curves for the 0-WS and W-0S be o b s e r v e d in these figures. With chamber
chambers are shown in Fig. 25, along with those shape fixed, combustion durations and duration
for the open and wedge chambers. Values of variations increased by 20-30 and 5 CA degrees,
openness for the 0-WS a n d W-0S chambers were respectively, when spark location was changed
4.2 and 12.2, respectively. For the open and from near-center to near-wall positions (open
wedge chambers, values of openness were 31.3 versus 0-WS a n d W-OS v e r s u s wedge chamber
and 5.6, respectively. Although the volume- curves in Figs. 28 a n d 29). With spark location
burned characteristics of t h e 0-WS and W-0S fixed, combustion d u r a t i o n s and d u r a t i o n v a r i a -
chambers fall outside the "openness" inference tions increased b y a b o u t 10 a n d l e s s t h a n 1 CA
space of this study, reasonable trend-wise degrees, respectively, when chamber shape was
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800459
14

a)
/o-ws
53-5

w
z
o
j= 3
<
<
W-OS
o-ws >- 2.5
W-OS,
"w m
o O

X
10 20 30 40 50 80 10 20 30 40 80
S P A R K A D V A N C E ( C A dug) S P A R K A D V A N C E (CAdeg)

Fig. 26 - Ignition delays for four chambers- Fig. 27 - Ignition delay variation for four
Labels show bounds on s p a r k advance (0.38 MBT to chambers. Labels show bounds o n spark advance
MBT) for each chamber (0.38 MBT t o MBT) for each chamber

[20 C =OPEN CHAMBER

Q5 O =OPEN CHAMBER -
O S O—WS CHAMBER •
a> O =0 — W S CHAMBER-
A = W — O S CHAMBER -
5 100 < 14 A =W — O S CHAMBER-
O =WEDGE CHAMBER' u O = W E D G E CHAMBER-
z 1 2

o
p 10
<
a: „
< 8
Q 40
>
3 20

X
10 20 30 40 60 10 20 30 40
S P A R K A D V A N C E { C A deg) S P A R K A D V A N C E (CA

Fig. 28 - C o m b u s t i o n durations for four cham- Fig. 29 - C o m b u s t i o n - d u r a t i o n variations for four

bers. Bounds on spark advance (.38 MBT to MBT) chambers. Bounds on spark advance (0.38 MBT to
shown o n e a c h curve MBT) chamber shown o n e a c h curve

altered from wedge to open configurations percentage points when chamber shape was altered
(wedge versus O-WS a n d W-OS v e r s u s open chamber from wedge to open configurations (wedge versus
curves in Figs. 28 a n d 2 9 ) . Uncertainties O-WS a n d W-OS v e r s u s open chamber curves in
associated with these estimates of combust ion Fig. 30). The uncertainty associated with
duration and d u r a t i o n variation are 6.0 and 1,6 these projections of IMEP variations Is 0.6%,
CA d e g r e e s , the RMS-errors of Eqs. 5 and 6, the RMS-error of Eq. 2.
respectively. Similar effects of spark Overall for the chamber configurations
location and chamber shape on e n g i n e performance considered, spark location appears to be the
stability were also observed. In light of the dominant factor, with more c e n t r a l location
strong relation between combustion and engine being desirable, whereas combustion chamber
stability described earlier, this should not be shape is also important, but has a smaller
a surprise. With chamber shape fixed, projected effect than spark location, With identical
IMEP variations increased by 5 to 7 percentage spark locations, either near-center or near-
points when spark location was moved from near wall, t h e wedge shape appears to be marginally
the center of the chamber to nearer the wall better than the open shape.
(open versus O-WS a n d W-OS v e r s u s wedge chamber DISCUSSION OF RESULTS
curves in Fig. 30). With spark location fixed, la this section the previously described
projected IMEP variations Increased by 1 to 2 results are summarized, and the implications of
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800459 15

_ 25 " conditions and chamber geometry on the combus-

• - OPEN CHAMBER - tion parameters were determined and are
g 2 0 - o 0 ~ O—WS CHAMBER T summarized In Table A.
gc Q \ A =W—OS CHAMBER - Each explanatory variable is described as
Q^ _ 15 \ \ C =WEDGE CHAMBER either primary, P, or secondary, S, depending
on the strength of its effect on the response
variable, as defined earlier. A directional
indication, either a (+) or (-), denotes the
direction in which the response variable changes
In response to an increase in an explanatory
vari able.
In the following discussion, reference is
made to propagation, burning, and expansion
velocities. These velocities are defined as:
1. Propagation velocity -- velocity,
relative to the cylinder head, at which the
S P A R K A D V A N C E { C A deg)
flame front propagates across the chamber.
2. Burning velocity -- v e l o c i t y , relative
Fig. 30 - IMEP variations for four chambers. to the unburned mixture, at which the flame
Bounds on spark advance (0.38 MBT to MBT) shown front engulfs the unburned mixture.
on e a c h curve 3. Expansion velocity — velocity,
relative to the cylinder head, at which the
burned region expands into the unburned region
because of the energy released during combus-
T a b l e k - Summary of O p e r a t i n g C o n d i t i o n s and Chamber Geometry tion.
E f f e c t s on Combustion As a result of these definitions the

Explanatory Variable Igni t i o n Delay Combustion D u r a t i o n instantaneous propagation velocity is the sum
Mean Variation Mean Variation of the instantaneous burning and expansion
velocities. During the early combustion period,
Residual F r a c t i o n P (+) P (+) P <+> P <+)
the flame propagation velocity is determined
Air-fuel Ratio
Spark Timi ng
p
p
w
(+)
P (+)
S <+)
P (+)
P (-)
P
S
(+)
(-) primarily by the expansion velocity component,
Engine Speed s {+) S {+) S (+) s (+) with a secondary contribution from the burning
Fueling Level s (-) s (-) S <-) s {-)
Chamber Openness __ -- P _){ p (-) velocity [29]. As the combustion progresses,
Chamber S q u i s h -- -- P (-> s (+) the role of the expansion velocity diminishes,
and the burning velocity becomes the important
factor.
these results with regard to improving engine The chemical factors, air-fuel ratio and
stability are discussed. residual fraction, are primary variables with
SUMMARY OF R E S U L T S - From the analyses of increasing effects (+)- o n both ignition delay
the relationships of combustion to engine and combustion duration. The expansion velocity
stability, it is apparent that improved engine component of the flame propagation velocity is
stability can be a c h i e v e d by speeding up and/or affected by the energy density of the mixture,
steadying the combustion process, i.e., decreas- increasing as the energy density increases
ing t h e means and/or cycle-to-cycle variations (less lean air-fuel ratio and/or decreased
of Ignition delay and combustion duration. By residual fraction) [29]. As a consequence, for
speeding up the combustion, more e n e r g y can be the same mass burned, a more e n e r g e t i c mixture
released at piston positions around top dead produces a greater burned volume. Assuming a
center, where the cylinder volume is not chang- spherical-type flame front, a larger flame
ing rapidly. Under these conditions the trans- front area is also obtained. On a n incremental
formation of cycle-to-cycle combustion varia- basis, this larger flame area produces a higher
tions to cylinder pressure variations is at a mass burning rate for each additional unit of
relative minimum. As more e n e r g y is released flame travel. The net result is faster combus-
later in the cycle, the cylinder pressure tion -- shorter ignition delay and combustion
variations reflect not only the combustion durat ion.
variations, but also changes in cylinder Adjustments of the chemical factors toward
volume. Fundamentally, a reduction of the less lean air-fuel ratios and/or lower residual
combustion variations translates directly Into fractions also have a steadying effect on the
improved engine stability. Although based on combustion. It is generally accepted that
data from specific open, wedge, and modified™ cyclic variations of in-cylinder mixture motions
wedge chambers, these conclusions should be cause variations in combustion. With higher
universally applicable to any chamber configura expansion velocities during the ignitiqn-delay
t ion. and early combustion-duration periods, the
For the specific chambers considered in relative effect of the cyclic mixture-motion
this study, the effects of the engine operating variations on the flame propagation is reduced.
 Downloaded from SAE International by University of New South Wales, Sunday, August 19, 2018

16 800459

Thus more stable combustion, as manifested by volume, either by shortening combustion periods
lower cyclic variations of ignition delay and or by advancing spark timing toward MBT timing.
combustion duration in this study, occurs as Improvements in engine stability obtained
the energy density of the mixture is increased. by adjusting the chemical factors — reducing
Physical operating conditions have mixed charge dilution with lowered air-fuel ratios
effects on c o m b u s t i o n . Spark advance, a primary and/or residual gases -- o c c u r because of both
variable in its effect on the mean combustion reduced combustion variations and improved
variables, has an increasing effect (+) on phasing of combustion to cylinder volume. In
ignition delay because of lower charge tempera- contrast, improvements of engine stability
tures and densities at the time of ignition, obtained by adjusting the physical factors of
but a decreasing effect (-) on combustion spark timing, fueling level, engine speed, and
duration, probably because of a more optimum chamber geometry, occur primarily because of
combination of pressures and temperatures better combustion-to-cylinder volume phasing,
during this main combustion period. In its generally occurring because of shortened
effects on c o m b u s t i o n variability, however, combustion periods. Of the physical factors,
spark timing is a secondary variable, having chamber geometry and spark timing variables
effects weaker, but directionally similar to, have the greatest influence on combustion and
its effects on the mean combustion variables. engine performance stability. Increased
Engine speed and fueling level are secondary openness, squish, and spark timing produce
variables having only weak e f f e c t s on engine Improved engine stability because of improved
combustion. Increasing engine speed results in combustion-to-volume phasing. An additional
longer and more unsteady combustion (on a benefit of greater openness ts a reduction of
crankangle basis). Although the real time of combustion variability. Spark timing has a
the combustion event is decreased because of similar, but weaker, effect on combustion
increased turbulence, this decrease is over- variations, whereas higher turbulence from
shadowed by an increase in the crankangle larger squish area has a weak, increasing
traveled per unit time (decreased cycle time) effect on these variations.
at higher engine speeds. For a given variation Of the two a p p r o a c h e s to reducing engine
i n real combust ion 11me, the larger crankang1e stability problems, improvement of the combus-
traveled per unit time at higher speeds also tion-to-volume phasing appears to be the most
results in larger crankangle variations of the practical, not because of the ease with which
combustion periods. Fueling level has a weak, this improvement can be achieved, but converse-
decreasing effect (-), with higher fueling ly, because of the difficulty involved with
levels producing generally shorter and steadier reducing combustion variability. As discussed
combustion. previously and summaried in T a b l e 4, variables
Both chamber geometry openness and squish having primary effects on c o m b u s t i o n varia-
are very significant physical factors. These bility were limited to air-fuel ratio, residual
geometric factors are primary variables having fraction, and combustion chamber openness.
decreasing effects (-) on c o m b u s t i o n duration. Because of practical limitations on the ranges
Combustion durations decrease because of (l) of air-fuel ratio and residual fraction,
more a c c e s s i b l e chamber volume associated with adjustments of these variables have limited
increased chamber openness, and (2) higher potential for controlling cyclic combustion
burning velocities associated with increased variations. In some e n g i n e s built for sale in
squish (and resulting higher turbulence). The California and in most future production
larger flame-front area early in the combustion engines, air-fuel ratio will be fixed at
period, which accompanies larger chamber stoichiometric to be c o m p a t i b l e with emission
openness, is probably also responsible for the control systems incorporating both reducing and
decreasing effect (-) of chamber openness on oxidizing catalysts. Fortunately, this mixture
combustion duration variations. With a larger strength is close to the value for minimum
flame area, the relative effect of local area engine instabilities. in calibrating engines,
variations caused by m i x t u r e motion variations levels of residual fraction are set, via levels
is reduced. Increased turbulence, deduced from of external EGR, to be c o n s i s t e n t with emissions
the effect of the squish parameter, appears to constraints. For lowest combustion variations,
have a weak, increasing effect (+) on combustion external EGR levels should be as low as possi-
duration variations. ble. Increased chamber openness has a greater
IMPROVING ENGINE PERFORMANCE STABILITY - potential for reduced variations of combustion.
From the above analyses of the engine-stability Equally important are the reduced combustion
path diagram, two a p p r o a c h e s can be taken periods which result from increased chamber
toward improving engine stability. One approach openness. Although not InvestIgated In this
is to reduce the combustion variability, the study, the potential for reducing cyclic varia-
fundamental cause of the engine stability tions of combustion through reduced variations
problem. The other approach is to attenuate of mixture motion should not be overlooked.
the effects of combustion variations by improv- Currently, however, the dependence of variations
ing the phasing of combustion-to-cylinder of mixture motion on e n g i n e geometry, including
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800459 17

intake manifolds, ports, and valves, are not Ignition delay is not affected by the chamber
well understood. Overall, adjustments of geometry. Greater openness (including the
physical factors, particularly chamber openness effect of better spark plug location) also
and turbulence-generating features of combus- leads to lower combustion duration variations,
tion chambers, to produce faster combustion whereas more squish (and presumably higher
appear to be the most practical and, at present, squish turbulence) appears to increase weakly
to have the greatest potential for improving these variations.
engine stabi1i ty. b. Advanced spark timing (up to MBT
timing) has a net effect of shortening the
SUMMARY combustion period (in CA d e g r e e s ) . Spark
timing has only a weak e f f e c t on combustion
Quantitative relationships which describe va r i a t ions.
the effects of combustion on e n g i n e performance c. Engine speed and fueling level
stability and of engine operating conditions appear to have weak effects on t h e combustion
and chamber geometry on c o m b u s t i o n characteris- (on a crankangle basis). In general, increased
tics have been established for the three engine speed increases both duration of combus-
chambers considered in this study. These tion and its variability. Fueling level has
relationships are provided in the text in the the opposite tendency.
form of model regression equations and corres-
ponding carpet plots. CONCLUSIONS
The relation between combustion and engine
performance stability indicates that improved Currently, the most practical approach for
engine stability can be o b t a i n e d by: improving engine stability is to shorten the
1. Reducing engine combustion variations, combustion event (on a CA b a s t s ) through
the fundamental cause of engine performance adjustments of physical factors, mainly chamber
variations. openness and turbulence-generating features.
2. Attenuating the strength of the Although more fundamental to the engine sta-
coupling between the combustion and engine bility problem, reduction of combustion
performance variations through improved variations Is more difficult to achieve.
combustion-cylinder volume phasing. This
improved phasing occurs when more e n e r g y Is ACKNOWLEDGMENTS
released at piston positions around top dead
center and can be o b t a i n e d by shortening the The author would like to thank R. R.
combustion event and by advancing the spark Toepel, formerly of the Engine Research Depart-
timing toward MBT timing. ment and currently with Detroit Diesel Allison
Although based on d a t a from three specific Division, a n d J . H. Tuttle, Engine Research
combustion chambers, the above observations Department, for supplying the engine test data
should apply to other chamber configurations as used in this study and for discussions of
well. Use o f the quantitative combustion- experimental procedures; J . C. DeSantis and E.
engine stability relationships for other G. Groff, Engine Research Department, for
chambers should also apply as long as the providing the volume burned-flame radius data
combustion inference space for these chambers for the three chambers; and D. I. Gibbons,
is similar the inference space of this study Mathematics Department, for helpful discussions
(see Append t x A). on RIDGE analysis and on the use of RIDGE
At a more fundamental level, combustion computer programs.
characteristics for improved engine stability
can be o b t a i n e d by a d j u s t m e n t s of operating REFERENCES
conditions and chamber geometry. For the open,
wedge, and modified-wedge chambers and the 1. G. A. Harrow, P. L. Orman, "A Study
operating conditions considered in this study: of Flame Propagation and Cyclic Dispersion in
1. Adjustments of chemical factors a Spark-Ignition Engine," Advanced School of
air-fuel ratio and residual fraction — toward Automotive Engineering (Part IV), Combustion
mixtures of greater energy density produce both Processes in the Spark Ignition Engine, Per-
shorter combustion events and smaller combus- gamon Press, July 1965-
tion variations (on a crankangle basis). 2. J . A. Warren, J . B. Hinkamp, "New
2. Adjustments of physical factors Instrumentation for Engine Combustion Studies,"
chamber openness and squish, spark timing, SAE Transactions, Vol. 64, 1956.
engine speed, and fueling level -- affect 3. S. Curry, "A Three Dimensional Study
primarily the mean c o m b u s t i o n characteristics of Flame Propagation in a Spark Ignition
and secondarily the combustion variations. Engine," SAE Transactions, Vol. 7 1 , 1963.
Chamber geometry and spark timing are the most 4. E. S. Starkman, F. M. Strange,
important physical factors. T. J . Dahm, " F l a m e Speeds and Pressure Rise
a. Greater chamber openness and in Spark Ignition Engines," SAE Paper No. 83V,
squish result in shortened combustion duration. 1959-
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18 800459

5. 0. Hirao, Y. Kim, "Combustion Varia- Symposium Volume on " C o m b u s t i o n Modeling in

tion Analysis on Flame Propagation in 4 Cycle Reciprocating Engines," November 6-7, 1978).
Gasoline Engines," Special Issue of JARt Tech- 21. V. L. Anderson, R. A. McLean, Design
nical Memorandum: Intermediate Reports of of Experiments, A Realistic Approach, Marcel
Combustion and Emission Researches, pp. 30-42, Dekker, Inc., New Y o r k , 1974.
Japan Automobile Research Institute, Inc., 22. N. H. Nie, C. H. Hull, J . G. Jenkins,
March 3970. K. Stelnbrenner, D. H. Bent, Statistical Package
6. S. Ohigashi, Y. Hamamoto, "Study on for the Social Sciences, Second Edition, McGraw-
Ignition Lag and Flame Propagation in Spark Hi11 Book Company, 1975.
Ignition Engines," Bulletin of the JSME, Vol. 23. G. M. Furnival, R. W. Wilson, Jr.,
13, No. 64, 1970. "Regressions by Leaps and Bounds," Technometrlcs
7. T. Mori, K. Yamazaki, "Variation in (16), pp. 499-5H, 1974.
the Flame Propagation Time in a Spark-IgnitIon 24. A. E. Hoerl, R. W. Kennard, "Ridge
Engine," Bulletin JSME, Vol. 13, No. 58, 1970. Regression: Biased Estimation for Nonorthogonal
8. M. Ogasawara, M. Matsuda, "Experi- Problems," Technometrics (12), pp. 56-67, 1970.
mental Research on Flame Propagation Delay in 25. G. C. McDonald, R. C. Schwing, " I n -
the Gasoline Engine with Electrical Ignition," stabilities of Regression Estimates Relating
Japan Society of Mechanical Engineers, Trans- Air Pollution to Mortality," Technometrics (15),
actions, Vol. 33 (245), 1967- • pp. 463-481, 1973.
9. B. D. Peters, G. L. Borman, "Cyclic 26. J . B. Heywood, R. J . Tabaczynski, "The
Variations and A v e r a g e Burning Rates in a S.I. Development of Performance Evaluation Criteria
Engine," SAE Paper No. 700064, 1970. for Lean Mixture Engines - Simultaneous Perform-
10. R. Vichnievisky, "Combustion in ance and Emissions Modeling of a Conventional
Petrol Engines," Proceedings of the Joint Spark-Ignition Engine," U.S. Department of Trans-
Conference on Combustion, IME-ASME, 1955. portation, Interim Report, Volume V, 1976.
11. G. A. Karim, "An Examination of the 27. R. B. Krieger, G. L. Borman, "The Com-
Nature of the Random C y c l i c Pressure Variations putation of Apparent Heat Release for Internal
in a Spark-Ignition Engine," J . of the institute Combustion Engines," ASME Paper No. 66-WA/
of Petroleum, Vol. 53, No. 519, March 1967. DGP-4, November 1966.
12. W. J . Anderson, S. S. Lestz, W. E. 28. G. M. Rassweiler, L. Withrow, "Motion
Meyer, "The Effect of Charge Dilution on CBC Pictures of Engine Flames Correlated with Pres-
Variations and Exhaust Emissions of an SI sure Cards," SAE Transactions, Vol. 42, Paper
Engine," SAE Paper No. 730152, 1973- No. 5, 1938.
13. R. K. Barton, D. K. Kenemuth, S. S. 29. J . N. Mattavi, E. G. Groff, F. A.
Lestz, W. E. Meyer, "Cycle-by-Cycle Variations Matekunas, "Turbulence, Flame Motion, and Com-
of a Spark ignition Engine - A Statistical bustion Chamber Geometry - Their Interactions
Analysis," SAE Paper No. 700488, 1970. in a Lean-Combustion Engine," GM Research
14. R. E. Winsor, D. J . Patterson, Publication GMR-2884, February 15, 1979 (also
"Mixture Turbulence - A Key to Cyclic Varia- in the Proceedings of I Mech E Conference on
tion," SAE Paper No. 730086, 1973. Fuel Economy and Emissions of Lean Burn
15. D. J . Patterson, "Pressure Variations, Engines, Paper C100/79, 1979).
A Fundamental Combustion Problem," SAE Paper No. 30. M. B. Young, J . H. Lienesch, "An
660129, 1966. Engine Diagnostic Package (EDPAC) - Software
16. J . P. Soltau, "Cylinder Pressure for Analyzing Cylinder Pressure-Time Data,"
Variations in Petrol Engines," Proceedings of SAE Paper No. 780967, 1978.
the Institution of Mechanical Engineers, No. 2,
1960-1961.
17. S. Sanda, T. Toda, H. Nohira, T. APPENDIX A - RANGE OF V A R I A B L E S AND RESULTANT
Konomi, "Statistical Analysis of Pressure Indi- INFERENCE SPACES
cator Data of an Internal Combustion Engine,"
SAE Paper No. 770882, 1977. The ranges of the explanatory variables of
18. G. H. Shtmoto, R. F. Sawyer, B. D. Figs. 3 and 4, along with their averages and
Kelly, "Characteristics of the Lean Misfire standard deviations, are s u m m a r i z e d -by tables
Limit," Report No. UCB-ME-77-2, University of and figures included in this Appendix.
California, Berkeley, January 1977. Combustion - Ranges of t h e e x p l a n a t o r y
19. J . H. Tuttle, R. R. Toepel, "Increased v a r i a b l e s o f F i g . 3 a r e shown i n F i g s . A - l
Burning Rates Offer Improved Fuel Economy-NOx t h r o u g h A-6 and a r e summarized i n T a b l e A - l .
Emissions Trade-offs in Spark-ignition Engines," Means and s t a n d a r d d e v i a t i o n s o f t h e e x p l a n a t o r y
SAE Paper No. 790388, 1979. v a r i a b l e s f o r the range of data t e s t e d a r e a l s o
20. J . N. Mattavi, E. G.'Groff, J . H. listed. Of p a r t i c u l a r i n t e r e s t i s t h e inter-
Lienesch, F. A. Matekunas, R. N. Noyes, "Engine a c t i o n of a i r - f u e l r a t i o w i t h r e s i d u a l s and
Improvements through Combustion Modeling," GM spark timing. The lower l i m i t o f residual
Research Publication GMR-2866, November 7, 1978 f r a c t i o n is about 0.10 (10%) o v e r the e n t i r e
"(also published in General Motors Laboratories air-fuel r a t i o range, whereas the upper limit
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800459 19

0.6 r 100 R
• = DATA B O U N D S
Q=DATA BOUNDS
o =OPEN CHAM.
o ^OPEN CHAM.
0.5 en &= W E D G E C H A M .
a = WEDGE CHAM.
•§80 0= M O D - W E D G E C H A M .
0= M O D - W E D G E C H A M .
<
cc
^0.3
<
90.2
to
tu
K
0.1

0.0
14 15 16 17 18 19 20 21 16 17 18 19
AIR-FUEL RATIO AIR-FUEL RATIO

Fig. A-l - Scatter plot of residual fraction vs Fig. A-2 - Scatterplot of spark timing vs. air-
air-fuel ratio fuel ratio

1.6 o = DATA BOUNDS

c=DATA BOUNDS
80 o = OPEN CHAM.
O = OPEN CHAM.
1.4
<±= W E D G E C H A M . a =WEDGE CHAM.
<a 0= M O D - W E D G E C H A M . 0= MOD-WEDGE CHAM.
X3
< 60
o CO

LU
U $ 1

| 40
>
a.
<
cc 20 % . 6

<
0.4 h
a.
0 0.2
0.00 0.10 0.20 0.30 0.40 0.50 14 15 16 17 18 19 20 21
R E S I D U A L FRACTION AIR-FUEL RATIO

Fig. A-3 - Scatterplot of spark timing vs. F i g . A-4 - S c a t t e r p l o t o f n o r m a l i z e d spark

residual fraction timing v s . air-fuel ratio

1.6
n= D A T A B O U N D S
c - OPEN CHAM. 0.06
O = DATA B O U N D S
1.4 -'• = W E D G E C H A M . o = OPEN CHAM.
-s^ M O D - W E D G E C H A M . d= W E D G E C H A M .
1.2
£ 0.05
o 0= MOD-WEDGE CHAM.
\
_j
1 3 0.04
_j
UJ
5 0.8
a.
> 0.03

z
_!
LU
0.4 - ^
LL

0.2 0.01
0.00 0.10 0.20 0.30 0.40 0.50 1200 1400 1600 1800 2000
RESIDUAL FRACTION E N G I N E S P E E D (r/min)

Fig. A-5 - S c a t t e r p l o t of normalized spark Fig. A-6 - Scatterplot of fueling level vs.
timing vs. residual fraction engine speed
 Downloaded from SAE International by University of New South Wales, Sunday, August 19, 2018

800459
20
60
O- D A T A B O U N D S
T a b l e A-i - Ranges of R e s i d u a l s and Spark Advances
o = O P E N CHAM.
? SO ^ - WEDGE CHAM
A! - f u e l Ses idual Spark Advance 0 = MOD-WEDGE
f\at io Fractio'i MBT Timing < CHAM.

1$ 0.10-0<4l 0.38-1.0 «;
16 0.10-0.38 0.38-1.0 uj 30
17 0.1O-G.35 0.3$-1.0 0
18 0-!0~0.32 0.38-1.0
O 20
19 0,10-0.29 Q.38~i.o
P
n = l?-3 0.220 0.671
De\ . - 1.6 O.077 § 10

O L j J 1 l 1 i L t _ l
20 30 40 50 60 70 80 90 100 110
C O M B U S T I O N D U R A T I O N ( C A deg)
varies with air-fuel ratio from 0.41 (4i|) at 15
to about 0.29 (291) at 19 a i r - f u e l ratio
(Fig. A-l). Similarly, limits of spark advance Fig. A-7 - Scatterplot of Ignition delay vs.
also vary wlth air-fuel ratio and res tdual combustion duration
fraction (Figs. A-2 and A - 3 ) . However, when
spark advance was normalized by MBT timing, the
limits of spark advance were constant over a 0= D A T A B O U N D S - —
range of 0.38 to 1.00 for all conditions (Figs. Q = OPEN CHAM. 0
A-4 a n d A-5)- s & =W E D G E CHAM.
Combinations of engine speeds aod fueling •° O- MOD-WEDGE CHAM.
levels included in the engine tests are shown
in Fig. A~6 a n d a r e summarized, atong with the z
means and s t a n d a r d d e v i a t i o n s of each variable, o
be l o w . § 4

Engine Speed Fueling Level Range

>
(r/min) (g/L/cycle) _ £ 2
1250 0.O3O-O.O3O
1400 0.022-0.037
0,018-0.041
_J 1
JOG 0.019-0.039 20 30 40 50 60 70
100 110
0.026-0.034 C O M B U S T I O N D U R A T I Of
2050 0.030-0.030

Mean 1712 0.033

Std. Dev. 0-007 Fig. A-8 - S c a t t e r p l o t of Ignition delay varia-
tion vs. combustion duration
Engine Stabllity - The distributions of
the explanatory combustion variables and abso-
lute spark advance are shown In Figs. A-/
through A-I1 and a r e summarized In Table A-2,
along with t h e means and standard deviations. 25 C = DATA BOUNDS
Because there is an o v e r l a p of combustion 0= O P E N C H A M .
£• - W E D G E C H A M .
duration, ignition delay, and v a r i a t i o n s of
delay and d u r a t i o n at different spark advances,
further subdivisions of these variables are
required at fixed spark timings and combustion
durations to define batter the inference space
of the engine stability regression equation.
These subdivisions are shown in Table A-3.

APPEND IX B GEOMETRIC PARAMETERS CONSIDERED

FOR U S E I N EGRESSIONS

Three combustion chambers open

30 40 50 60 70 80 100 110
a n d mod i f l e d - w e d g e configurations (Fig. 2)
COMBUSTION DURATION
were of interest in this study. Many parameters
can be d e f i n e d to characterize combustion
chamber geometry. The g e o m e t r i c parameters
that are important in any study depend on the Fig, A~9 - Scatterplot of combustion duration
response variables of interest. In this study, variation vs. combustion duration
 Downloaded from SAE International by University of New South Wales, Sunday, August 19, 2018

800459 21

0 = DATA BOUNDS
2
0 =OPEN CHAM. • = DATA B O U N D S
< ~ W E D G E CHAM. g> o = OPEN CHAM.
Q O = MOD-WEDGE CHAM. •o a =WEDGE CHAM.
< 6 - O = MOD-WEDGE CHAM.

CD

Q i I I 1 I i I I I I 01 I I I I I I I I i I
20 30 40 50 60 70 80 90 100 110 0 5 10 15 20 25 30 35 40 45 50
C O M B U S T I O N D U R A T I O N ( C A deg) I G N I T I O N D E L A Y ( C A deg)

Fig. A-10 - S c a t t e r p l o t of normalized ignition Fig. A-ll - Scatterplot of ignition delay

delay vs. combustion duration variation vs. ignition delay

T a b l e A-2 - Ranges o f Combustion V a r i a b l e s and Spark Advance* T a b l e A-3 - F u r t h e r S u b d i v i s i o n s o f Combustion Variables

and S p a r k Advance*
Spark Combustion Igni t i o n Delay Duration
Advance Duration Delay Variation Variation
Spark Combust ion 1gn i t ion Delay Duration
35~60 10-19 1-2 2.0-7
Advance Duration Delay Variation V a r i a t ion
IS
25 35-70 13-24 1.2-3.5 2.5-12
35 35-90 18-30 2-5 4-15 15 35 10-19 1-2 2-4
45 40-100 24-35 2.2-5 5~J4 *5 to-19 1-2 2-7
60 60-70 30-43 3-5 8-17 55 12-19 1-2 4-7
Mean 31.6 59-8 22.9 2.85 8.63
25 35 13-19 1.2-2 2.5-4
Dev. 11.6 U.3 6.90 1.11 4.01
45 13-24 1.2-3 2.5-7
•• U n i t s I n t a b l e a r e c r a n k a n g l e degrees 55 13-24 1.2-3.5 4-10
65 15-24 1.7-3-5 6-12

35 35 18 2 4
45 18-25 2-3 4-6
55 18-30 2-4 4-10
normalized intake-valve annulus area, squish,
65 18-30 2-5 6-13
normalized maximum f l a m e - t r a v e l distance at top
75 18-30 2.3-5 8-15
dead center, and a parameter characterizing the 85 22-30 3-5 11-15
chamber "openness" were used as candidate
45 40 24-24 2.2-2.5 5-6
explanatory variables in the regression analy- 50 24-30 2.2-3-3 5-9
ses. Intake valve areas and s q u i s h were used 60 24-35 2.2-4.6 5-12
as relative measures of chamber turbulence. 70 24-35 2.2-5 7-14
Maximum flame travel distance was used as a 80 24-35 2.6-5 10-15
90 24-35 3.2-5 12-15
relative indicator of spark plug location. The
100 24-32 4-4 14-14
openness parameter, d e f i ned b e l o w , was used to
quantify the a c c e s s i b i l i t y of the contents of " Units in t a b l e are crankangle degrees
each chamber to a spherical flame propagating
from the spark plug.
The normalized intake-valve area variable,
with a 5% d i f f e r e n c e between maximum a n d mini- the ratio of constants "a" to "m" of Wiebe
mum v a l u e s , was not statistically significant functions ( E q . B-l) which were used to describe
in the a n a l y s e s . Similarly, the normalized volume-burned fraction versus normalized flame
maximum flame-travel distance, with values of radius curves (see F i g . 5 for typical curves).
0.59, 0.87, and 0.37 for the open, wedge, and The significance of the "a t o m" ratio Is
modified-wedge chambers, was not significant. described below. Voiume-burned fraction curves
It should be n o t e d that the openness parameter were obtained by g e o m e t r i c calculations of
includes an e f f e c t of spark plug location. volumes of spheres with different radii (flame
Squish, the percent bore area for which the radii) centered at the spark plug and inter-
clearance distance was equal to the gasket cepted by the cylinder head, piston crown, and
thickness, was found to be s i g n i f i c a n t . Squish cylinder walls. At any piston position, the

values were 0%, 5-8%, and 16% f o r the open, series of volumes of spheres with radii ranging
from zero to t h e maximum f l a m e travel distance
wedge, and modified-wedge chambers, respective-
were used to chart the progress of the spherical
ly. Chamber openness was a significant geomet-
flame as it traveled across the chamber.
ric variable. This variable was d e f i n e d to be
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800459
22

Values of openness for the three chambers were WIEBE FUNCTION PARAMETERS
determined by least-squares fitting computed Open Wedge Mod i f r e d - w e d g e
volume-burned fraction versus flame radius data Parameter Chamber C hambe r Chamber
for each chamber configuration at piston top "a" 20.94 8.29 9.39
dead center to a Wiebe function of form: "m" 1.85 1.47 1.51
a/m 11.3 5.6 6.2
V /V t = 1 - exp ( -a ( r/r b ) 1 , 1 + 1
) (B-l)
APPENDIX C - DETERMINATION OF COMBUSTION
where V/V^ is the volume-burned fraction VARIABLES
r is the flame travel distance
(radius of spherical flame The mass-burned fraction curve, a cumula-
front) tive time history of t h e mass burned in the
r^ is the diameter of the cylinder cylinder, was used to characterize the engine
bore combustion. The heat release analyses of
a,m are parameters to be determined Krieger-Borman (K-B) [27] and Rassweiler-
Withrow (R-W) [28] were used to compute this
Parameter "m" describes the shape of the curve from measured cylinder pressure-time data.
Wiebe curve. With "a" fixed, steeper rising In the K-B analysis, rates of mass burned are
curves, i.e., greater volume-burned fraction inferred from an energy balance among the work
per unit flame travel, have lower values of done, heat losses, change in internal energy of
"m". Parameter "a" is related to the maximum the charge, and fuel energy released during
flame travel distance, with larger "a" corres- the combustion. In addition to the cylinder
ponding to shorter distances. Thus parameter pressure data, detailed specifications of the
"a" is very sensitive to the spark plug loca- engine operating conditions, charge composition,
tion. The ratio " a / m " was chosen as a single and cylinder heat transfer characteristics
quantitative measure of the relative chamber are required input to the analysis. In the
openness. Increased a/m, because of increased R-W a n a l y s i s , the total change in cylinder
"a" or decreased "m" or both, reflects increased pressure is separated into the components due
accessibility of the unburned mass to the to piston motion and combustion. The mass-
propagating flame. The volume-burned fraction burned fraction curve is determined by assuming
data for the open, wedge, and modified-wedge that the fraction of total combustion pressure
chambers are shown in Fig. B-l (symbols) along change o c c u r r i n g In any time interval starting
with the corresponding least-squares-fit Wiebe at ignition was caused by the burning of an
function curves (1Ines). The parameters for equal fraction of the total combustible mass.
these Wiebe curves are listed below. The more The only input to this analysis Is the measured
desirable location of the spark plug in the pressure data phased to cylinder volume. In
open chamber is clearly shown in Fig. B-l, comparison to the K-B method, this analysis
where t h e maximum flame travel distance is 60% trades accuracy for simplicity.
of the bore dimension, and by the large value Results from the two heat release analysis
of "a" below. techniques for the same a v e r a g e pressure data
are compared in Figs. C-l and C-2, where the
R~W values of ignition delay and combustion

F L A M E R A D I U S / C Y L I N D E R B O R E - R/R B 0 R E K-B I G N I T I O N D E L A Y - C A

Fig. C-l - Comparisons of Ignition delays

Fig. B-l - Comparison of Wiebe function fits computed w i t h the Krieger-Borman [27] and
(lines) with actual volume burned-flame radius Rassweiler-Wtthrow [28] heat release analyses on
data (symbols) identical pressure files
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800459 23

K - B C O M B U S T I O N DURATION - CA

Fig. C-2 - Comparisons of combustion durations

computed w i t h the Krieger-Borman [27] and
Rassweiier-Withrow [28] heat release analyses on
identical pressure files

duration are plotted against the K-B values. the K-B analysis of the average pressure cycles
The solid lines in the figures indicate where to form o v e r a l l average combustion parameters,
the points would fall if there were perfect and were included in the data base described
correlation. Overall the K~B ignition delays in the text. Although more a c c u r a t e than the
and combustion durations were slightly shorter R-W a n a l y s i s , the complexity of the K-B heat
and longer, respectively, than the R-W counter- release requi res longer computational times.
parts. As a consequence, the K-B method is usually
Combustion parameters of interest in this applied to the average pressure cycles [30].
study were the averages and variations of igni- However because combustion parameters are not
tion delay and combustion duration. The R-W linearly related to the cylinder pressures,
analysis technique was used to determine the analysis of the average pressure cycles wi11
ignition delays and combustion durations of the not necessarily yield the same v a l u e s for these
96 individual pressure cycles recorded at each parameters as averaging the results from the
test point. Standard deviations of the delays analysis of the 96 individual pressure cycles.
and durations computed from these results were The o v e r a l l average delays and durations
used to quantify the combustion variations. described above were formed to reduce the un-
The averages of the 96 individual delays and certainty associated with determining the
durations were combined w i t h the results from "correct" values for these parameters.
 Downloaded from SAE International by University of New South Wales, Sunday, August 19, 2018

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