Vapor Cycles

Course Outcomes

• Ability to acquire and explain the basic

concepts in thermodynamics.

• Ability to apply and correlate the concept with

the appropriate equations and principles to the appropriate equations and principles to

analyze and solve engineering problems.

Course Learning Outcomes

The student should be able to:

• Describe the principles of carnot vapor cycles and its impracticalities

• Explain the principles of an ideal rankine power cycle

• Explain how pressure and temperature affect thermal efficiency of an ideal rankine power cycleefficiency of an ideal rankine power cycle

• Explain the principle of the reheat Rankine power cycles.

• Sketch the T-s diagram for carnot,ideal rankine and ideal reheat rankine cycles.

• Solve problems related to ideal rankine and reheat rankinecycles.

8.1 Carnot Vapor Cycle

8.2 Rankine Vapor Cycle

8.3 Reheat Rankine Cycle

8.1 Carnot Vapor Cycle

It is most efficient cycle operating between two specified temperature limits BUT it IS

NOT a suitable model for power cycles, BECAUSE:

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

the impingement of liquid droplets on the turbine blades causing erosion and wear.

Process 4-1 It is not easy to control the condensation process so precisely to achieve

T-s diagram of two Carnot vapor cycles.

Process 4-1 It is not easy to control the condensation process so precisely to achieve

quality at point 1. And it is not practical to design a compressor that handles two

phases. 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

Those problems can be eliminated by executing Carnot cycle in

figure (b), HOWEVER this cycle presents other problem.

� isentropic compression to extremely high pressures

� isothermal heat transfer at variable pressures.

Conclusion

� Carnot cycle cannot be approximated in actual devices� Carnot cycle cannot be approximated in actual devices

� It is not realistic model for vapor power cycles

IDEAL CYCLE for vapor power cycle is

RANKINE CYCLE

8.2 Rankine Vapor Cycle

Impracticalities associated with the Carnot cycle can be eliminated by

� superheating the steam in the boiler and

� condensing it completely in the condenser.

The ideal Rankine cycle does not involve any internal irreversibilities.

The simple ideal Rankine cycle.

Energy Analysis of the Ideal Rankine Cycle

Steady-flow energy equation

( ) ( )in o u t o u t in e iq -q - w -w = h - h (k J/k g )

The thermal efficiency can be interpreted as the ratio of the area enclosed

by the cycle on a T-s diagram to the area under the heat-addition process.

Example 10.1Consider a steam power plant operating on the simple ideal Rankine cycle.

Steam enters the turbine at 3 MPa and 350°C and is condensed in the

condenser at a pressure of 75 kPa. Determine the thermal efficiency of this

cycle.

Problem 10.22

Consider a steam power plant that operates on a simple ideal A

simple Rankine cycle and has a net power output of 45 MW.

Steam enters the turbine at 7 MPa and 500°C and is cooled in the

condenser at pressure of 10 kPa by running cooling water from

the lake through the tubes of condenser at rate of 2000 kg/s.

i. Show the T-s diagram with respect to saturation linei. Show the T-s diagram with respect to saturation line

ii. Determine the thermal efficiency of the cycle

iii. Determine the mass flowrate of the steam

iv. Determine the temperature rise of the cooling water.

HOW CAN WE INCREASE THE EFFICIENCY OF THE RANKINE

CYCLE?

To increase the thermal efficiency…

� 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.

Lowering the Condenser Pressure

(Lowers Tlow,avg)

Superheating the

Steam to High Temperatures

(Increases Thigh,avg)

(Lowers Tlow,avg)

Increasing the Boiler Pressure

(Increases Thigh,avg)

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 this pressure depending on the temperature of

the cooling medium � cannot be lower than Psat

corresponding to the temperature of the cooling

medium.

Side effect: Lowering the condenser pressure

increases the moisture content of the steam at

the final stages of the turbine.

Superheating the Steam to High Temperatures (Increases

Thigh,avg)

Both the net work and heat input increase

as a result 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.

The effect of superheating the

steam to higher temperatures on

the ideal Rankine cycle.

Side effect: 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

highest steam temperature allowed at the

turbine inlet is about 620°C.

Increasing the Boiler Pressure (Increases Thigh,avg)

For a fixed turbine inlet temperature,

the cycle shifts to the left and the

moisture content of steam at the

turbine exit increases. This side effect

can be corrected by reheating the

steam.

Today many modern steam power

plants operate at supercritical

pressures (P > 22.06 MPa) and have

thermal efficiencies of about 40% for

fossil-fuel plants and 34% for nuclear

plants.

The effect of increasing the boiler

pressure on the ideal Rankine cycle.A supercritical Rankine cycle.

Example 10.3

Consider a steam power plant operating on the ideal Rankine cycle. Steam

enters the turbine at 3 MPa and 350°C and is condensed in the condenser at a

pressure of 10 kPa.

Determine:

(a) The thermal efficiency of this power plant

(b) The thermal efficiency if steam is superheated of 600°C instead of 350°C

(c) The thermal efficiency if the boiler pressure is raised to 15 MPa while the (c) The thermal efficiency if the boiler pressure is raised to 15 MPa while the

turbine inlet temperature is maintained at 600°C.

8.3 Reheat Rankine Cycle

How can we take advantage of the increased efficiencies at higher

boiler pressures without facing the problem of excessive

moisture at the final stages of the turbine?

Answer:Answer:

1. Superheat the steam to very high temperatures.

� It is limited metallurgically.

2. Expand the steam in the turbine in two stages, and reheat it in

between (reheat)

The ideal reheat Rankine cycle.

Additional info.:

• The single reheat in a modern power plant

improves the cycle efficiency by 4 to 5% by

increasing the average temperature at which

heat is transferred to the steam.

• The average temperature during the reheat

process can be increased by increasing the

number of expansion and reheat stages �

approach an isothermal process at the

maximum temperature. The use of more

than two reheat stages is not practical. The

The average temperature at which heat is

transferred during reheating increases as the

number of reheat stages is increased.

than two reheat stages is not practical. The

theoretical improvement in efficiency from

the second reheat is about half of that which

results from a single reheat.

• The reheat temperatures are very close or

equal to the turbine inlet temperature.

• The optimum reheat pressure is about one-

fourth of the maximum cycle pressure.

What is the purpose of reheat cycle?

Example 10.4

Consider a steam power plant operates on the ideal reheat Rankine cycle.

Steam enters the high-pressure turbine at 15 MPa and 600°C and is

condensed in the condenser at a pressure of 10 kPa. If the moisture content of

the steam at the exit of the low-pressure is not to exceed 10.4 percent,

determine:

(a) The pressure at which the steam should be reheated

(b) The thermal efficiency of the cycle(b) The thermal efficiency of the cycle

Assume the steam is reheated to the inlet temperature of the high-pressure

turbine.