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L 31
Rankine Cycle with Enhancements
Dr. Gore
Example
520°C, 140 bar
520°C (40 bar)
1
3
Turbine 2
5
Turbine 1
0.08 bar
4
40 bar
2
250°C (140 bar)
7 bar
H. P. F. W. Pump
140 bar
7 bar
7 bar
12
0.08 bar
O.F. W.H.
9
10
•
•
L. P. F. W. Pump
Throttle
40 bar
•
7
8
C. F.W.H.
•
6
7 bar
11
The components of a modern Rankine cycle power plant include a steam generator, multiple reheaters, multiple stages of turbines, a condenser, a cooling tower, multiple feed water pumps,
an open feed-water heater and multiple closed feed water heaters, multiple feed water pumps,
and throttling devices for feeding back of the extracted steam into the feed water system.
The example shown above is for illustration purposes and each plant is typically custom
designed for the local conditions and customer requirements. In the example shown above,
superheated steam at state 1 is generated by the steam generator that is receiving
of heat
from a combustion furnace typically burning coal, natural gas, oil, biomass or all of the above
depending on the fuel availability, prices, power management needs, environmental
requirements, incentives and subsidies, and management decisions.
The heat generated by combustion of the fuel is transferred to the feed water which enters the
steam generator as a sub-cooled liquid at state 12 (140 bar and 250 oC) and leaves as
superheated vapor at state 1 (140 bar and 520 oC). The processes in the steam generator
include sub-cooled heating from (140 bar and 250 oC) to (140 bar and 336.75 oC) in a gas to
liquid heat exchanger, boiling from saturated liquid to saturated vapor state at a fixed
temperature of 336.75 oC in a drum and tube or a tube and tube boiler, and then superheating
from 336.75 oC to 520 oC in a gas to gas extended surface shell and finned tube heat exchanger
portion of the steam generator.
The transfer of heat from the combustion gases at high temperature to the water and steam at
lower temperature involves significant net entropy production and loss of exergy. One of the
areas of opportunity is to reduce the temperature difference across which combustion gases
transfer heat to the steam and water.
1
•
•
•
•
•
•
•
•
The superheated steam at high temperature and pressure is expanded in the high pressure
turbine to produce work by conversion of enthalpy to kinetic energy in an impulse stage of
nozzles and then of the kinetic energy to work represented by the rate of change of angular
momentum multiplied by the angular displacement per unit time of the turbine wheel. The
turbine rotor drives the rotor of a generator which supplies electricity to the consumers. In
steady state, the work of the turbine matches the work of the generator. In a real system, the
steam flow is modulated at many frequencies by a complex interconnected control system that
also includes depositing and recovering stored energies from a flywheel system to maintain the
60 Hz frequency of electrical power even in the face of fluctuating load demand. With the
introduction of renewable energy sources into the grid, power plant controls engineering has
become a great area of opportunity for ME300 graduates.
The high pressure turbine expands the steam from 140 bar to 40 bar in as close to an isentropic
manner as possible. If the expansion can be accomplished in an isentropic manner, the exit
temperature is 320 oC and the state is superheated (Tsat = 250.4 oC).
The exit steam flow from the HPT is divided into two streams. One stream flows to a steam reheater which raises the temperature to 520 oC but now at a lower pressure. The other stream
flows into a closed feed water heater which reduces the temperature by heating the 140 bar
high pressure feed water that is flowing through tubes of the heat exchanger. The shell side
steam cools to the saturated liquid state in the process and the liquid is extracted to flow
through a throttle for mixing in the low pressure (8 bar) open feed water heater.
The portion of the steam at 40 bar reheated to 520 oC expands to 7 bar through the first stage of
the low pressure turbine producing work. At this stage, a portion of the steam is extracted for
open system heating of the feed water pumped to 7 bar pressure. The remaining steam
expands through the final stage of the low pressure turbine to the condenser pressure of 0.08
bar producing additional work.
In the condenser the mass of steam leaving the final low pressure turbine stage is cooled by a
circulating water stream in a noncontact heat transfer process to generate saturated liquid at
0.08 bar and 41.51oC. The heat rejected in the condenser
is an important part of the
overall system energy balance. Further, the second law of thermodynamics requires that a
certain percentage of the heat added in the steam generator plus the heat added in the reheater must be rejected in the condenser. The saturated liquid stream leaving the condenser at
0.08 bar is pumped by the low pressure feed water pump to 7 bar before entering the open feed
water heater. The three streams mixing in the open feed water heater restore the mass flow
rate of water flowing through the high pressure feed water pump to that of the flow rate
through the indirect contact feed water heater and the steam generator.
The heat rejected by the condenser is deposited into the environment by either a cooling tower
or a flowing river stream in the vicinity of the power plant.
Many auxiliary devices are necessary for metering, controlling, regulating various pressures,
temperatures and flows. These are not shown or considered here in the first level of power
plant analysis.
The plant definition summarized above allows the first level of cycle analysis on the basis of
balance equations for mass, energy and exergy. The analysis and insights can be improved by
studying the processes on a T-s diagram.
2
1
3
12
9
10
2s
11
8
4s
7
6
5s
T-s diagram for the Rankine cycle showing two turbine stages with reheating and extractions for
feed water heating are depicted above.
•
•
•
•
•
•
Isentropic turbines assumed for simplicity
4, 11, 7 mix in the open feed water heater to make 8.
9 is Heated to 12 using energy given up in the process 2 to 10
Note the mass of cold substance in feed water heaters is much higher that the mass of hot
substance. (Unlike regenerators in Brayton cycle where the masses are similar).
Pitting of turbine blades is caused by impinging drops at relatively high velocities, when
expansion process leads to condensation of liquid drops.
A part of the (small) expanded steam is used to preheat the water going into the boiler. This
action increases the average temperature of heat addition and efficiency. (This is analogous to
using exhaust gasses of a turbine to preheat air in a Brayton cycle). Fully expanded steam can’t
be used for this purpose because it is already at a very low temperature and heat recovery from
it for regeneration is impossible.
3
•
•
Pump work is generally very small compared to turbine work. Typically pumps are driven using
small steam turbines attached to them rather than connected mechanically to the shaft of the
main steam turbine. Electrical motors may also be used to drive pumps.
Cogeneration plants tap steam off at an appropriate location (lower the pressure the better) for
heating for processing applications.
State p,
bar
1
140
2s
40
T, oC
3
4
5
6
7
8
9
40
7
0.08
0.08
7
7
140
520
10
11
12
40
7
140
•
(1
•
7.15
•
Remark
520
320
3378.7
3015.4
Use Given ,
320°% & '() *+,()(- ./+') (40 bar)
3490.0
2975.0
41.51 2240.5
41.51 173.88
~42
174.58
~165 697.22
~165 711.25
6.4610
6.4610
(6.4553)
7.15
7.15
7.15
0.5926
-
250.4 1087.3
~165 1087.3
~
1175
-
Energy analysis on F.W.H. performed
Energy analysis on F.W.H. performed
Energy analysis on F.W.H. performed
71 8( 9 : ;1 < 71 =(>
0.86 B
ST
.∆V
1
: ;1 < 0.86=
0.86
H. IJ
0.86;2577= : ;0.14=173.88
>
;1.0084 W 10 0 =;7 < 0.08=100
0.6978
⁄
LLMH. N OP/OR
(Note pump work is small.)
(-)/Y /- 1 & Y[ /- 11 & Y\ /- 4 & ,V)] ^))_ S/-)` )/-)` /]/+a(b(.
;1 < Y[ < Y\ =
G
;C. 1 D.1E F=
;G. GC D.1E F=
71 ;8.2287= : ;1 < 71 =0.5926 B 71
71
Assume 1
Use given 0 , 0 (approximate interpolation)
approximate interpolation
Use (1 7.15 , (Saturated because (1 6 ( )
Saturated liquid (0.08 bar)
Pump work is added
Energy analysis on F.W.H. performed using these
Energy analysis on F.W.H. performed using
>
/- 7 c/`( ],S],
D
> dD efg
C
d b(
: Y[
: Y\
],S],
C b(
d
1;
G=
],S]. Y\ , Y[ ,
h 1087.3
Still 2 Unknowns: Closed feed water heater analysis
1;
<
E=
Y[ ;
<
D=
250°% Use Table A-5 Compressed Liquids Table
1175
/]_, Y\
;ijk il =
;ik ijm =
; Y[
0.152
697.22 :
;
E
. DG
;140
DDD
G
0.241
: ST
< 7=100
G
: .G ;140 < 7=100
697.22 : 14.73
4
711.95
/`) /- - b( V,b]- ']' ],S].