A. Beccari
S. Beccari
E. Pipitone
1
e-mail: pipitone@dima.unipa.it
Department of Mechanics,
University of Palermo,
Palermo 90128, Italy
An Analytical Approach for the
Evaluation of the Optimal
Combustion Phase in Spark
Ignition Engines
It is well known that the spark advance is one of the most important parameters influ-
encing the efficiency of a spark ignition engine. A change in this parameter causes a shift
in the combustion phase, whose optimal position, with respect to the piston motion,
implies the maximum brake mean effective pressure for given operative conditions. The
best spark timing is usually estimated by means of experimental trials on the engine test
bed or by means of thermodynamic simulations of the engine cycle. In this work, instead,
the authors developed, under some simplifying hypothesis, an original theoretical formu-
lation for the estimation of the optimal combustion phase. The most significant param-
eters involved with the combustion phase are taken into consideration; in particular, the
influence of the combustion duration, of the heat release law, of the heat transfer to the
combustion chamber walls, and of the mechanical friction losses is evaluated. The the-
oretical conclusion, experimentally proven by many authors, is that the central point of
the combustion phase (known as the location of the 50% of mass fraction burnt, here
called MFB50) must be delayed with respect to the top dead center as a consequence of
both heat exchange between gas and chamber walls and friction losses.
DOI: 10.1115/1.3155395
1 Introduction
The phasing of the combustion process with respect to the pis-
ton motion is one of the most important parameters influencing
the torque provided by a spark ignition SI engine. Since this
combustion phase depends on the spark ignition timing, located at
the so called ignition angle, the control upon this angle is very
important to obtain the best performance in every operative con-
dition.
Two different approaches are commonly followed for the deter-
mination of the maximum brake torque MBT spark timing: The
first is based on experimental trials at the engine test bed, which
can be performed by either maximizing the engine torque see,
e.g., Refs. 1–3 or setting a “combustion phase indicator” which
is a parameter derived from in-cylinder pressure analysis and as-
sumes reference fixed values when the combustion timing is op-
timal 4 to its best value 5–7. The second approach, instead,
proceeds by means of simulations based on a thermodynamic
model of the engine 8–11, which, endowed of appropriate sub-
models for combustion 12, heat transfer 13, and friction loss
8,14,15 modeling, allow the brake mean effective pressure
bmep estimation once the spark advance is fixed. For each en-
gine operative condition, the best combustion phase can be found
by means of successive trials. In this paper, instead, the authors
propose an original theoretical approach to the problem of the
determination of the optimal combustion phase in spark ignition
engines.
With reference to the working cycle of the engine compression
and expansion strokes during a crankshaft rotation from -180 deg
to +180 deg with respect to the top dead center TDC, the an-
gular phase of the heat introduction Q
1
that grants the maximum
torque first depends on the way the combustion takes place i.e.,
on the heat release law and then on the effects of the heat Q
1
upon the various thermodynamic variables involved.
The theoretical approach proposed can be carried out at differ-
ent approximation levels with respect to the following hypothesis:
a unsteady, ideal, zero-dimensional evolution of a perfect
gas in the combustion chamber
b adiabatic engine i.e., no heat exchange between the gas
and the chamber walls
c constant specific heat capacity c
v
of the gas
d instantaneous combustion
e combustion length
c
=
b
-
a
, being
a
and
b
the
crank angular positions at the starting and ending of the
combustion process
f presence of heat transfer between the gas and the cham-
ber walls
g presence of friction losses
2 Gas Temperature Trend During Combustion
Considering that previous hypotheses a–c and e are true, it
is quite simple to evaluate the gas temperature trend versus the
crank angular position . Ignoring the gas speed and the subse-
quent viscous friction losses, it is possible to write the first and the
second laws of thermodynamics during the infinitesimal combus-
tion time dt, corresponding to the crank rotation angle d, in
which the gas receives the combustion specific heat dQ
in
:
dQ
in
= c
v
dT + pdv = c
v
dT + RT
dv
v
= TdS 1
where T, v, p, S, c
v
, and R are the gas temperature, specific vol-
ume, pressure, specific entropy, constant volume specific heat, and
gas constant, respectively.
Assuming that
=
R
c
v
1
v
dv
d
=
k -1
v
dv
d
1
Corresponding author.
Contributed by the Internal Combustion Division of ASME for publication in the
JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received
September 11, 2008; final manuscript received May 21, 2009; published online
November 24, 2009. Review conducted by Christopher J. Rutland.
Journal of Engineering for Gas Turbines and Power MARCH 2010, Vol. 132 / 032802-1
Copyright © 2010 by ASME
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