Page 135 - Entrophy Analysis in Thermal Engineering Systems

128 Entropy Analysis in Thermal Engineering Systems

a low temperature is discharged to the atmosphere. A regenerator is
employed to preheat the working fluid before it is pressurized by the feed
pump. The thermodynamic model of the cycle can be built up using a
set of energy conservation and entropy balance equations described in the
preceding section for the steam cycle.
The total entropy generation rate of the ORC is obtained by

_ X _ _ _
Φ ORC ¼ Φ i + Φ g,L + Φ c,L (8.60)
where i denotes the components of the ORC, and
_
_ Q g,L
Φ g,L ¼ HF HF (8.61)
0 S
+ S
T 0 out
where S 0 denotes the entropy flow of the hot fluid at the ambient temper-
HF
ature and pressure, and S out is its entropy flow at the outlet of the evaporator.
HF
The amount of heat discharged by the hot fluid to the environment is deter-
mined using Eq. (8.62).
_ HF HF (8.62)
Q ¼ H H 0
g,L
out
The thermal efficiency of the cycle is evaluated as follows.

η ¼ _ W net (8.63)
HF HF
H H
in
out
Fig. 8.15 shows the thermal efficiency and the total entropy generation rate
varying with the extraction pressure, p 6 , for three typical working fluids.
The results in Fig. 8.15 are obtained using the data given in Table 8.7.
The efficiencies of the pumps and turbine are assumed to be the same as
those in Table 8.4. The main observation in Fig. 8.15 is that the thermal
efficiency inversely correlates with the entropy generation rate for all three
fluids. A design based on the maximum thermal efficiency is therefore
equivalent to that of minimum entropy generation rate.
Notice that the specific entropy generation method is inapplicable for the
case of ORC, because the thermal energy is supplied through a hot stream,
unlike the cycles examined in the previous sections that are driven by fuel
combustion. The inverse correlation between the cycle efficiency and the
entropy generation rate for the ORC of Fig. 8.13 is due to the fixed heat
input supplied to the cycle via the hot fluid; see Chapter 7, Section 7.7.
The reader may also return to Chapter 6, Section 6.5 for the analysis of
the Carnot vapor cycle with fixed heat input.