BITS Pilani
Vapor Power Cycle
In this chapter
• Ideal vapor power cycle- Comparison Carnot cycle or Rankine cycle?
• Thermodynamic analysis of Rankine cycle
• Methods to increase efficiency
- Reheat
- Regeneration
-- Open feedwater heaters and closed feedwater heaters
- Cogeneration
- Combined power cycle
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Carnot cycle
• Ideal cycle vs actual cycle
- Ideal cycle is reversible
- Carnot cycle – Only a theoretical construct
French physicist Sadi
Carnot in 1824
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Significance of Carnot cycle
It is the cycle with maximum theoretical efficiency and thus can be used as a
standard against which efficiencies of all other actual cycles can be compared.
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Ideal vapor cycle
Carnot cycle : Difficulties Rankine cycle : ideal vapor cycle
• Difficult to compress two phase • Steam is condensed completely
mixture (process 4-1) and then pumped (process 1-2)
• Steam can be superheated to
• Low quality steam at turbine exit –
increase quality at turbine exit
damages turbine parts (state 3) (state 4)
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Analysis of Rankine cycle
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Numerical example
Consider an ideal Rankine cycle with saturated vapor entering the turbine at 8 MPa
and exits the condenser as saturated liquid at 0.0075 MPa. The cycle has a net
power output of 100 MW. Determine
(a) the thermal efficiency,
(b) the back work ratio,
(c) the mass flow rate of the steam, in kg/h,
(d) the rate of heat transfer, , into the working fluid as it passes through the boiler, in
MW,
(e) the rate of heat transfer, from the condensing steam as it passes through the
condenser, in MW
(f) the mass flow rate of the condenser cooling water, in kg/ h, if cooling water enters
the condenser at 15C and exits at 35C.
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Actual cycle
Actual cycle including irreversibilities Actual cycle ignoring irreversibilities
associated with all the processes in boiler and condenser
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Numerical – actual cycle
Consider the earlier problem with turbine and pump isentropic efficiency of 85% and
determine all the parameters mentioned earlier.
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Increasing efficiency of
Rankine cycle
Lowering condenser Superheating the steam Increasing boiler pressure
pressure (lowers Tavg of (Increases Tavg of heat (Increases Tavg of heat
heat rejection) addition) addition)
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Rankine cycle with reheat
Consider an ideal Rankine cycle with reheat where the steam enters the first turbine at 10
MPa, 480 C and expands to a pressure of 0.7 MPa. It is then reheated to a temperature of
440 C before entering the second turbine where it expands to a condenser pressure of
0.0075 MPa. The net power output is 100 MW. Determine (a) the thermal efficiency of the
cycle, (b) the mass flow rate of steam, in kg/h, (c) the rate of heat transfer from the
condensing steam as it passes through the condenser, in MW.
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Regeneration (open feedwater
heater)
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OFWH example
Consider a steam power plant operating on Rankine cycle with regeneration and reheat.
Steam entering the turbine is at a pressure of 10 MPa with a temperature of 550C. It leaves
the first turbine at 0.8 MPa. Some steam is extracted at this pressure and sent to an open
feedwater heater. The remaining steam is reheated to 500C and sent to the second turbine
where it expands to 10 kPa before entering the condenser. Determine the mass flow rate
through the boiler and the thermal efficiency of the cycle. The power output is 80 MW.
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Regeneration (closed
feedwater heater with pump)
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CFWH example
Repeat the earlier OFWH problem, by replacing the OFWH with a CFWH. Assume that the
FW leaves the heater at the condensation temperature of the extracted steam and the
extracted steam leaves the FWH as saturated liquid and is pumped to the line carrying
feedwater.
Consider a steam power plant operating on Rankine cycle with regeneration and reheat.
Steam entering the turbine is at a pressure of 10 MPa with a temperature of 550C. It leaves
the first turbine at 0.8 MPa. Some steam is extracted at this pressure and sent to an open
feedwater heater. The remaining steam is reheated to 500C and sent to the second turbine
where it expands to 10 kPa before entering the condenser. Determine the mass flow rate
through the boiler and the thermal efficiency of the cycle. The power output is 80 MW.
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Comparison OFWH - CFWH
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Types of CFWH
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CFWH with steam trap instead of pump and
mixing-chamber
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Multiple FWH
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Multiple FWH Example 1
Consider a reheat–regenerative vapor power cycle with two feedwater heaters, a closed
feedwater heater and an open feedwater heater. Steam enters the first turbine at 10 MPa, 450
C and expands to 0.8 MPa. The steam is reheated to 400C before entering the second turbine,
where it expands to the condenser pressure of 0.01 MPa. Steam is extracted from the first
turbine at 2 MPa and fed to the closed feedwater heater. Feedwater leaves the closed heater at
200 C and 10 MPa, and condensate exits as saturated liquid at 2 MPa. The condensate is
trapped into the open feedwater heater. Steam extracted from the second turbine at 0.3 MPa is
also fed into the open feedwater heater, which operates at 0.3 MPa. The stream exiting the
open feedwater heater is saturated liquid at 0.3 MPa. The net power output of the cycle is 100
MW. There is no stray heat transfer from any component to its surroundings. If the working
fluid experiences no irreversibilities as it passes through the turbines, pumps, steam generator,
reheater, and condenser, determine (a) the thermal efficiency, (b) the mass flow rate of the
steam entering the first turbine, in kg/h.
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Example 2
Q1.A Consider a regenerative vapor power cycle with two feedwater heaters, a closed one
and an open feedwater heater. Steam enters the first turbine stage at 12 MPa, 480C, and
expands to 2 MPa. Some steam is extracted at 2 MPa and fed to the closed feedwater
heater. The remainder expands through the second-stage turbine to 0.3 MPa, where an
additional amount is extracted and fed into the open feedwater heater operating at 0.3
MPa. The steam expanding through the third-stage turbine exits at the condenser pressure
of 6 kPa. Feedwater leaves the closed heater at 210C, 12 MPa, and condensate exiting as
saturated liquid at 2 MPa is trapped into the open feedwater heater. Saturated liquid at 0.3
MPa leaves the open feedwater heater. Assume all pumps and turbine stages operate
isentropically. Determine for the cycle (a) the heat transfer to the working fluid passing
through the steam generator, in kJ per kg of steam entering the first stage turbine. (b) the
thermal efficiency. (c) the heat transfer from the working fluid passing through the
condenser to the cooling water, in kJ per kg of steam entering the first-stage turbine.
ANS (a) 2395.7 KJ/Kg (b) 45.9% (c) 1297.1 KJ/Kg
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Cogeneration
What is cogeneration? (also called Industrial Process Heating)
Energy required by process industry – Thermal , electrical
Typically, for any processing industry, 2/3rd of energy required is thermal and 1/3rd
electrical.
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Cogeneration applications
Glycol boilers – Natural gas/ Calendar rolls – Manufacture of
crude oil refineries smooth paper/textile sheet
Chemical, pulp and paper, oil production and refining, steel making, food processing,
textile industries and district heating (domestic heating)
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Cogeneration
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Cogeneration (contd.)
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T-s diagram for process
heating
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Numerical - cogeneration
Consider a cogeneration power plant modified with regeneration. Steam enters the turbine
at 9 MPa and 400 C and expands to a pressure of 1.5 MPa. At this pressure,
35 percent of the steam is extracted from the turbine, and the remainder expands to 10
kPa. Part of the extracted steam is used to heat the feedwater in an open feedwater heater.
The rest of the extracted steam is used for process heating and leaves the process heater as
a saturated liquid at 1.5 MPa. It is subsequently mixed with the feedwater leaving the
feedwater heater, and the mixture is pumped to the boiler pressure. Assuming the turbines
and the pumps to be isentropic, show the cycle on a T-s diagram with respect to saturation
lines, and determine the mass flow rate of steam through the boiler for a net power output
of 25 MW. Also determine the utilization factor.
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