Environmental Engineering Reference
In-Depth Information
beginning of the compression stroke to
v
c
at the end (1
→
2), followed by a constant-volume
heating (2
3) to replicate the adiabatic combustion of the fuel-air mixture, then an isentropic
expansion to the maximum volume
→
v
e
, after which a constant-volume cooling (4
→
1) completes
the cycle (a process which is absent in the open cycle ICE).
The net cyclic work
w
, equivalent heat added
q
, and thermodynamic efficiency
η
th
for the Otto
cycle are
w
=
pd
v
=
Tds
3
q
=
Tds
2
Tds
3
2
η
th
=
(3.38)
Tds
The Otto cycle efficiency is a monotonically increasing function of the volumetric compression
ratio,
v
e
/v
c
, and, of course, the thermodynamic properties of the working fluid. For simplifying
assumptions about the working fluid, it may be expressed as
1
(v
e
/v
c
)
(
c
p
/
c
v
)
−
1
η
th
=
1
−
(3.39)
For a typical gasoline engine compression ratio of 9 and
c
p
/
5%.
In gasoline engines, the compression ratio is limited by the tendency of the fuel-air mixture
to combust spontaneously (called
knock
). A higher compression ratio is used in the diesel engine,
where the fuel is injected after the air is compressed, providing a greater thermodynamic efficiency
for the diesel engine compared with the gasoline engine.
Because the Otto cycle is a model for the reciprocating ICE, the amount of equivalent heat
q
is limited by the amount of fuel that can be burned in the fuel-air charge in the cylinder at
the end of the compression stroke. The combustible fuel is a maximum when the air/fuel ratio is
stoichiometric, which is the normal condition for gasoline engines.
18
The maximum temperature
T
3
at the end of combustion is thus the adiabatic combustion temperature of the compressed mixture
in the cylinder.
19
Because the reciprocating ICE engine experiences this peak temperature only
momentarily and is otherwise exposed to a much lower average temperature, it is able to operate
successfully with peak temperatures that exceed the melting point of most materials and secure the
favorable thermodynamic efficiencies that accompany such high temperatures.
The thermodynamic efficiencies of automotive engines are noticeably less than the ideal ef-
ficiency of equation (3.39). Friction of pistons and bearings, power required to operate valves,
cooling pump, and the fuel supply system, pressure losses in intake and exhaust systems, and
c
v
=
1
.
26,
η
th
=
43
.
18
In gasoline engines the load is varied by changing the pressure
p
1
and thus the amount of stoichiometric
fuel-air mixture in the cylinder. In diesel engines, the air pressure is fixed but the amount of fuel injected is
varied.
19
In the Otto cycle model of the ICE, combustion occurs at constant volume. The constant-volume fuel
heating value and adiabatic combustion temperature are not exactly the same as those for constant-pressure
combustion, but the differences are small.
