Page 372 - Advanced thermodynamics for engineers

16.5 FRICTION IN RECIPROCATING ENGINES 361

where ^ p is the maximum cylinder pressure and N ¼ engine speed (rev/min). Other models for fmep are
discussed in Stone (2012).
The Chen and Flynn equation is a relatively simple expression containing speed and load terms.
The coefficients are evaluated from experimental results, and the terms based on engine speed are
normally more significant than those for maximum pressure. Hence, at constant engine speed, the fmep
is almost a constant, and not dependent on the engine power output (bmep or imep).

16.5.1 THE EFFECT OF FRICTION ON OPTIMUM COMPRESSION RATIO
If an Otto engine is free to work without a peak pressure ð^ pÞ limitation then the maximum efficiency is
achieved with high compression ratios (r) (see Chapter 3, Eqn (3.16)), i.e.

1
h ¼ 1
th
r ðk 1Þ
However, high compression ratios can result in very high peak pressures, and these might cause
detonation of the gas at the end of combustion (called the end gas) as well as high mechanical stresses.
If the Otto cycle is limited in peak pressure then the situation changes and the compression ratio for
maximum efficiency will occur when the full pressure rise is achieved by compression: however, the
work output will be zero, as discussed in Chapter 6. If friction is included the situation changes yet
again and a compression ratio resulting in the maximum brake thermal efficiency can be evaluated.
Consider that the fmep is constant (at a particular speed), then the compression ratio for maximum
thermal efficiency, with a fixed peak pressure, can be evaluated.
For an Otto cycle, shown in Fig. 16.8
p 2 ¼ p 1 r k (16.22)

T 3
p 3 ¼ p 2 (16.23)
T 2
Hence energy addition/unit mass

q 23 ¼ c v T 3 T 2 (16.24)
Now

T 2 ¼ T 1 r k 1 and T 3 ¼ p 3 T 2 ¼ ^ p k T 2 ¼ a k T 2 ;
p 2 p 1 r r
^ p
where a ¼
p 1
n a o
giving q 23 ¼ c v T 1 r k 1 1 (16.25)
r k
By definition, indicated work/unit mass

1 k 1 n a o
w i ¼ h q 23 ¼ 1 k 1 c v T 1 r k 1 (16.26)
th
r r