Page 264 - The Mechatronics Handbook

0066_frame_C12 Page 29 Wednesday, January 9, 2002 4:22 PM

piston during the power stroke, would produce the same net work as actually developed in one cycle.
That is,

mep = net work for one cycle (12.31)
-----------------------------------------------------
displacement volume
where the displacement volume is the volume swept out by the piston as it moves from the top dead
center to the bottom dead center. For two engines of equal displacement volume, the one with a higher
mean effective pressure would produce the greater net work and, if the engines run at the same speed,
greater power.
Detailed studies of the performance of reciprocating internal combustion engines may take into
account many features, including the combustion process occurring within the cylinder and the effects
of irreversibilities associated with friction and with pressure and temperature gradients. Heat transfer
between the gases in the cylinder and the cylinder walls and the work required to charge the cylinder
and exhaust the products of combustion also might be considered. Owing to these complexities, accurate
modeling of reciprocating internal combustion engines normally involves computer simulation.
To conduct elementary thermodynamic analyses of internal combustion engines, considerable simpli-
fication is required. A procedure that allows engines to be studied qualitatively is to employ an air-
standard analysis having the following elements: (1) a fixed amount of air modeled as an ideal gas is the
system; (2) the combustion process is replaced by a heat transfer from an external source and represented
in terms of elementary thermodynamic processes; (3) there are no exhaust and intake processes as in an
actual engine: the cycle is completed by a constant-volume heat rejection process; (4) all processes are
internally reversible.
The processes employed in air-standard analyses of internal combustion engines are selected to represent
the events taking place within the engine simply and mimic the appearance of observed pressure-displace-
ment diagrams. In addition to the constant volume heat rejection noted previously, the compression stroke
and at least a portion of the power stroke are conventionally taken as isentropic. The heat addition is
normally considered to occur at constant volume, at constant pressure, or at constant volume followed by
a constant pressure process, yielding, respectively, the Otto, Diesel, and Dual cycles shown in Table 12.7.
Reducing the closed system energy balance, Eq. (12.7b), gives the following expressions for work and
heat applicable in each case shown in Table 12.7:

--------- = u 1 – u 2 , --------- = u 3 – u 4 , -------- = u 1 – u 4 (12.32)
Q 41
W 34
W 12
m m m
Table 12.7 provides additional expressions for work, heat transfer, and thermal efficiency identified with
each case individually. All expressions for work and heat adhere to the respective sign conventions of
Eq. (12.7b). Equations (1) to (6) of Table 12.4 apply generally to air-standard analyses. In a cold air-
standard analysis the specific heat ratio k for air is taken as constant. Equations (1′) to (6′) of Table 12.4
apply to cold air-standard analyses, as does Eq. (4′) of Table 12.5, with n = k for the isentropic processes
of these cycles.
Referring to Table 12.7, the ratio of specific volumes v 1 /v 2 is the compression ratio, r. For the Diesel
cycle, the ratio v 3 /v 2 is the cutoff ratio, r c . Figure 12.8 shows the variation of the thermal efficiency with
compression ratio for an Otto cycle and Diesel cycles having cutoff ratios of 2 and 3. The curves are
determined on a cold air-standard basis with k = 1.4 using the following expression:

k
1
r c –
1
η = 1 – -------- -------------------- ( constant k) (12.33)
r k−1 kr c –( 1)
where the Otto cycle corresponds to r c = 1.

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