Page 370 - Advanced thermodynamics for engineers

16.5 FRICTION IN RECIPROCATING ENGINES 359

16.5 FRICTION IN RECIPROCATING ENGINES
The basic equation defining the variation of thermal efficiency of an engine operating on the Otto cycle
was derived in Chapter 3, and is from Eqn 3.16

1
h ¼ 1
th
r ðk 1Þ
This thermal efficiency is the indicated thermal efficiency. The more important parameter for the
engine user is brake thermal efficiency, because this relates the energy input in the fuel to the power
output at the crankshaft. The brake thermal efficiency is defined as

h ¼ h h (16.17)
th m
b
where h m is the mechanical efficiency. The mechanical efficiency accounts for all the losses between
the fuel input and the power output, and includes friction, effects of heat loss, and ‘pumping work’,
when the gas is flowing through the valves.
brake work bmep p b
h ¼ ¼ ¼ (16.18)
m
indicated work imep p i
The value of mechanical efficiency changes over the operating range of the engine. If the engine is
idling then the mechanical efficiency is zero because the brake output is zero. The efficiency is
maximum at a high power output. A typical value of maximum mechanical efficiency for a
reciprocating engine is between 80% and 90%: it is very dependent on the rating (bmep) of the engine.
While mechanical efficiency appears to be a useful measure of losses in reciprocating engines, it is
better to evaluate these losses using the friction mean effective pressure (fmep). Equation (16.5) relates
imep to work output by
H
pdV
p ¼
i
V s
where p is the imep.
i
The area of the large rectangle in Fig. 16.8 is equal to that of the p–V diagram, because p V s has the
i
same area as 1-2-3-4-1.
Also shown on Fig. 16.8 are the brake mean effective pressure (bmep), p , and the fmep, p . These
f
b
can be related to the imep by
p ¼ p þ p : (16.19)
b
i
f
While imep can be evaluated directly from the p–V, or indicator diagram, fmep and bmep usually
have to be evaluated from the output of the engine on a dynamometer. It is relatively easy to evaluate
the bmep of an engine using the following equation for power output, P,inkW
p V s n cyl n cyc p LAn cyl n cyc p LAn cyl N cyc
b
b
b
P ¼ ¼ ¼ kW; (16.20)
1000 1000 60 1000
where
L ¼ stroke (m)
2
A ¼ bore area (m )