181)
INTERNAL
COMBUSTION
ENGINE FUNDAMENTALS
assumed
fixed):
ub3
=
350
-
118.2
-
2956
x
0.031
=
140
kJ/kg air
With
v3
=
0.125
m3/kg
air, Fig.
4-8
gives
po
=
7270
kPa,
T3
=
2890
K
Expand at constant entropy to
v,
=
1
m3/kg air:
p,
=
595
kPa,
T,
=
1920
K,
u,
=
-
1457
kJ/kg
air
W3.,
=
WE
=
1597
kJ/kg air
Continue expansion at constant entropy to the exhaust pressure,
p,
=
1
atm:
v,
=
4
m3/kg air,
T,
=
1360
K
Equation
(5.17)
now gives the residual fraction
which agrees with the value assumed for the second iteration.
The fuel conversion efficiency can now
be
calculated:
where
n,
=
kg fueI/kg air at state
I
=
(:)(I
-
XJ
Thus
The indicated mean effective pressure is
5.53
CI
Engine Cycle Simulation
With a diesel engine fuel-air cycle calculation, additional factors must
be
taken
into account. The mixture during compression is air plus a small amount
of
residual gas. At point
2
liquid fuel is injected into the hot
compressed
air at
temperature T2;
as
the fuel vaporins and heats up, the air
is
cooled. For
a
constantsolume mixing process which is adiabatic overall, the mixture intemd
energy is unchanged, i.e.:
mf
cu/,
+
c,,G
-
To11
+
ma~v,a(~,
-
T,)
=
0
(5.53)
IDEAL
MODELS
OF
ENGINE
CYCLES
181
mf
is the mass of fuel injected,
uf,
is the latent heat of vaporization of the
fuel,
cVqf
is the specific heat at constant volume of the fuel vapor,
7''.
is the
mixture temperature (assumed uniform) after vaporization and mixing is com-
plete, ma
is
the mass of air used, and c,, is the specific heat at constant volume of
air. substitution of typical values for fuel and air properties gives
(T,
-
T,.)
x
70
K
at full load. Localized cooling in a real engine will be greater.
The limited-pressure cycle is a better approximation to the diesel engine
than the ~~IIStant-p~eSSUre or constant-volume cycles.
Note that because nonuniformities in the fuel/air ratio exist during and
after combustion in the
CI
engine, the burned gas charts which assume uniform
composition will not
be
as
accurate an approximation to working fluid properties
as they are for
SI
engines.
5.53
Results of Cycle Calculations
Extensive results of constant-volume fuel-air cycle calculations are available.'.
3.
"
Efficiency is little affected by variables other than the compression ratio
r,
and
equivalence ratio
4.
Figures 5-9 and 5-10 show the effect of variations in these
two parameters on indicated fuel conversion efficiency and mean effective pres-
sure. From the available results, the following conclusions can be drawn:
1.
The effect of increasing the compression ratio on efficiency at a constant
equivalence ratio is similar to that demonstrated by the constant
y
constant-
volume cycle analysis (provided the appropriate value of
y
is used; see Fig.
5-19).
2.
As the equivalence ratio is decreased below unity (i.e., the fuel-air mixture is
made progressively leaner than stoichiometric), the efficiency increases. This
occurs because the burned gas temperatures after combustion decrease,
decreasing the burned gas specific heats and thereby increasing the effective
value of
y
over the expansion stroke. The efficiency increases because, for a
given volume-expansion ratio, the burned gases expand through a larger tem-
perature ratio prior to exhaust; therefore, per unit mass of fuel, the expansion
stroke work is increased.
3.
As the equivalence ratio increases above unity (i.e., the mixture is made pro-
gressively richer than stoichiometric), the efficiency decreases because lack of
sufficient air for complete oxidation of the fuel more than offsets the effect of
decreasing burned gas temperatures which decrease the mixture's specific
heats.
4.
The mean effective pressure, from Eq. (5.2), is proportional to the product
dqf,,.
This exhibits a maximum between
4
=
1.0 and
4
%
1.1, i.e., slightly rich
of stoichiometric. For
4
less than the value corresponding to this maximum,
the decreasing fuel mass per unit displaced volume more than offsets the
increasing fuel conversion e(frdency. For
4
greater than this value, the
decreasing fuel conversion eficiency (due to decreasing combustion efficiency)
more than offsets the increasing fuel mass.