Solution Cycle Analysis and Rankine Cycles
1
5
8
High Pressure
Turbine (T1)
Low Pressure
Turbine (T2)
Condenser
Pump
(P1)
Steam
Generator
Feedwater
Heater
Pump
(P2)
2
3
4
6
7
A steam power plant operates
on an ideal reheat-
regenerative Rankine cycle
shown on the left. All the
steam flows into the high-
pressure turbine. At the exit
of this turbine, some of the
steam is extracted and sent to
the feedwater heater. The rest
of the steam is reheated and is
expanded in the low pressure
turbine.
Some of the data for this cycle
are shown in the table below.
(1) Complete the table using
appropriate cycle idealizations
(2) Find the cycle efficiency.
Point
1
2
3
4
5
6
7
8
P (MPa)
0.01
0.8
0.8
10
10
0.8
0.8
0.01
h (kJ/kg)
191.78
192.60
720.68
730.94
3500.9
2811.9
3480.6
2494.40
s (kJ/kg∙K)
0.6487
0.6487
2.0450
2.0450
6.7561
6.7561
7.8673
7.8673
From the cycle idealization that there is no pressure in heat transfer devices and mixing devices,
we see that P2 = P3 = P6 = P7 = 0.8 MPa, P4 = P5 = 10 MPa, and P8 = P1 = 0.01 kPa. The
pressures found from these idealizations are shown in the table in italics. Additional values for
entropy and enthalpy values to complete the table are found below. These are also displayed in
the table in italics.
Because the feedwater heater has a mixture of liquid and vapor, the cycle idealization for point
three is that it is a saturated liquid. This gives h3 = hf(0.8 MPa) = 720.68 kJ/kg, s3 = 2.0450 kJ/kg,
and v3 = 0.001115 m3/kg. The cycle idealizations, all work devices are isentropic gives the
following results: s2 = s1 = 0.6487 kJ/kg, s4 = s3 = 2.0450 kJ/kg, s6 = s5 =6.7561 kJ/kg, and s8 = s7
= 7.8673 kJ/kg. The only value remaining to be filled in the table is h4 which can be found from
an analysis of the second pump. For isentropic processes in a liquid we can compute the work
as the integral of vdP, assuming that v is constant. This gives
kg
kJ
mkPa
kJ
kPakPa
kg
m
PPvwP
26.101
80010000
001115.0
3
3
343
2
We then find h4 = h3 + |wP2| = 720.68 kJ/kg + 10.26 kJ/kg = 730.94 kJ/kg.
In this cycle there are three distinct mass flow rates at different points in the cycle. The entire
flow, which occurs from the exit of the feedwater heater to the exit of the high-pressure turbine
can be set to 1. At this point, the flow that goes to the steam generator to be reheated can be set
to f, and the remaining flow, that goes to the feedwater heater must be 1 – f to give a mass
balance. Using this unit flow and the variable f to represent the split, the flow rates at various
points in the cycle have the values shown below. (Here,
a
m6
represents the mass flow into the
feedwater heater.)
1
543 mmm
fmmmm 2187
fm a1
6
docsity.com
