Lecture W06

Dr. Ammar Tariq

Vapor and Combined Power Cycles

Chapter 10
The Carnot Vapor Cycle
➢ The Carnot cycle is the most efficient cycle operating between two
specified temperature limits.
➢ Consider the cycle shown on T-s curve
➢ Note that it is not a suitable model for vapor
power cycles owing to the following reasons:
➢ Process 1-2: Limiting the heat transfer
processes to two-phase systems severely
limits the maximum temperature that can be
used in the cycle (374°C for water)
➢ Process 2-3: The turbine cannot handle
steam with a high moisture content because of 1-2 isothermal heat addition in a
the impingement of liquid droplets on the boiler
2-3 isentropic expansion in a
turbine blades causing erosion and wear. turbine
➢ Process 4-1: It is not practical to design a 3-4 isothermal heat rejection in a
compressor that handles two phases. condenser
4-1 isentropic compression in a
compressor
The Carnot Vapor Cycle

➢ T-s diagrams of another possible Carnot cycle is shown:

➢ This cycle is also not suitable for vapor power cycle since
it requires:
➢ Isentropic compression to extremely high pressures and
➢ Isothermal heat transfer at variable pressures.

Here again:
1-2: isothermal heat addition in a boiler
2-3: isentropic expansion in a turbine
3-4: isothermal heat rejection in a condenser
4-1: isentropic compression in a compressor
Rankine Cycle: The Ideal Cycle for Vapor Power Cycles

➢ Many of the impracticalities associated with the

Carnot cycle can be eliminated by:
➢ Superheating the steam in the boiler and

➢ Condensing it completely in the condenser.

➢ The cycle that results is the Rankine cycle,

which is the ideal cycle for vapor power plants.
➢ The ideal Rankine cycle does not involve any
internal irreversibility.
Rankine Cycle: The Ideal Cycle for Vapor Power Cycles

1-2 Isentropic compression in a pump

2-3 Constant pressure heat addition in a boiler
3-4 Isentropic expansion in a turbine
4-1 Constant pressure heat rejection in a condenser
Rankine Cycle (Thermodynamic Analysis)
Steady-flow energy equation
1-2 Pump 3-4 Turbine
2-3 Boiler 4-1 Condenser

The efficiency of power plants in the U.S. is often expressed in terms

of heat rate, which is the amount of heat supplied, in Btu’s, to generate
1 kWh of electricity. (Note that 1 Btu = 1.0551 kJ)
= (h2 – h1)
rbw = (3.03  713.1) = 0.004
Deviation of Actual Vapor Power Cycles from Idealized Ones
➢ The actual vapor power cycle differs from the ideal Rankine
cycle because of irreversibilities in various components.
➢ Fluid friction and heat loss to the surroundings are the two
common sources of irreversibilities.
Isentropic efficiencies

(a) Deviation of actual vapor power cycle from the ideal

Rankine cycle. (b) The effect of pump and turbine
irreversibilities on the ideal Rankine cycle.
Deviation of Actual Vapor Power Cycles from Idealized Ones
➢ Fluid friction causes pressure drops in the boiler, the condenser, and the piping
between various components.
➢ As a result, steam leaves the boiler at a somewhat lower pressure.
➢ Also, the pressure (P3) at the turbine inlet is somewhat lower than that at the boiler
exit due to the pressure drop in the connecting pipes.
➢ The pressure drop in the condenser is usually very small.
➢ To compensate for these pressure drops, the water must be pumped to a
sufficiently higher pressure than the ideal cycle calls for.
➢ This requires a larger pump and larger work input to the pump.
➢ Heat loss from the steam to the surroundings as the steam flows through various
components.
➢ To maintain the same level of net work output, more heat needs to be transferred to
the steam in the boiler to compensate for these undesired heat losses.
➢ As a result, cycle efficiency decreases.
➢ Note that due to irreversibilities the processes are non-isentropic and:
➢ Pump requires greater work input
➢ Turbine produces lower work output
How can we increase the efficiency of the Rankine Cycle?
➢ The basic idea behind all the modifications to increase the thermal
efficiency of a power cycle is the same, i.e:
➢ Increase the average temperature at which heat is transferred to the
working fluid in the boiler, or
➢ Decrease the average temperature at which heat is rejected from the
working fluid in the condenser.
➢ This purpose can be achieved by any one of the following THREE
methods:
➢ Lowering the Condenser Pressure (Lowers Tlow,avg)
➢ Superheating the Steam to High Temperatures (Increases Thigh,avg)
➢ Increasing the Boiler Pressure (Increases Thigh,avg)
How can we increase the efficiency of the Rankine Cycle?
1. Lowering the Condenser Pressure (Lowers Tlow,avg)
➢ To take advantage of the increased
efficiencies at low pressures, the
condensers of steam power plants
usually operate well below the
atmospheric pressure.
➢ There is a lower limit to this pressure
depending on the temperature of the
cooling medium.
Side effect: Lowering the condenser
pressure increases the moisture content
The effect of lowering the condenser
pressure on the ideal Rankine cycle. of the steam at the final stages of the
turbine.
How can we increase the efficiency of the Rankine Cycle?
2. Superheating the Steam to High Temperatures (Increases Thigh,avg)

➢ Both the net work and heat input

increase because of superheating the
steam to a higher temperature. The
overall effect is an increase in thermal
efficiency since the average temperature
at which heat is added increases.
➢ Superheating to higher temperatures
decreases the moisture content of the
steam at the turbine exit, which is
desirable.
➢ The temperature is limited by
metallurgical considerations. Presently
The effect of superheating the the highest steam temperature allowed
steam to higher temperatures on at the turbine inlet is about 620°C.
the ideal Rankine cycle.
How can we increase the efficiency of the Rankine Cycle?
3. Increasing the Boiler Pressure (Increases Thigh,avg)
For a fixed turbine inlet temperature, the Today many modern steam power plants
cycle shifts to the left and the moisture operate at supercritical pressures (P >
content of steam at the turbine exit 22.06 MPa) and have thermal efficiencies
increases. This effect can be achieved by of about 40% for fossil-fuel plants and 34%
reheating the steam. for nuclear plants.

The effect of increasing the boiler

pressure on the ideal Rankine cycle.