Modern Engineering Thermodynamics

470 CHAPTER 13: Vapor and Gas Power Cycles
back into a much hotter boiler. By reducing a major irreversibility of the cycle, the overall thermal efficiency of
the cycle is increased.
Regenerative feedwater heating is shown schematically in Figure 13.20. These regenerators are simply heat
exchangers. There are two common types:
a. Open loop (or direct contact) heat exchangers, in which the regeneration vapor mixes directly with the boiler
feedwater.
b. Closed loop heat exchangers, in which the regeneration vapor and the boiler feedwater do not mix until after
the regeneration vapor has been condensed into a liquid.
As an example of regeneration thermodynamics, consider the open loop regenerative feedwater heater shown in
Figure 13.20a. These units were normally adiabatic (all the heat transfer occurs internally) and aergonic. A steady
state, steady flow mass and energy rate balance (neglecting any changes in potential or kinetic energy) on the
regenerator yields
and
Combining these two equations to eliminate _m 4 gives
_m 4 + _m 5 − _m 6 = 0
_m 4 h 4 + _m 5 h 5 − _m 6 h 6 = 0
h 6 = ð1 − yÞh 4 + yh 5
whereweusey = _m 5 / _m 6 = _m 5 / _m 1 as the mass fraction of regeneration vapor extracted from the prime mover.
Solving for y produces
where
y = h 6 − h 4
h 5 − h 4
(13.11)
h 4 = h 3 + v 3 ðp 4 – p 3 Þ/ðη s Þ pump1
Pump 2
6
7
m
Boiler
5
Regenerator
1
my
4 3
Pump 1
Prime mover
Stage
1
Stage
2
Condenser
W E
2
m(1–y)
7
6a
1 Prime mover
m
Stage Stage W E
Boiler
1 2
5
my
2
4a
m(1 – y)
4 3
Regenerator
Condenser
Pump 1
Pump 2
6
(a) Open loop regeneration
(b) Closed loop regeneration
T
4
3
7 m 1
6
my
m(1 – y)
2s 2
5
T
7
4a
6a m
4 6 my
m(1 – y)
3
1
2s 2
5
s
Open loop
(c) Thermodynamic diagram
s
Closed loop
FIGURE 13.20
The Rankine cycle with regeneration.