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S.1 Superheat and Reheat

The basic steam cycle works with saturated steam. This leads to some important issues:

Limited thermal efficiency. According to the definition of

the Carnot cycle, the efficiency of a cycle grows if heat is supplied at higher temperatures and rejected at lower temperatures.

Saturated steam does not provide very high temperature in the cycle, as higher temperature means higher pressure and there are constraints regarding material strength in the boiler.

Also, the higher the pressure at the turbine outlet, the wetter is the steam (for fixed condenser pressure), and thus there is significant risk for blade erosion in the turbine.

In this chapter, two modifications of the basic steam cycle are presented, which allow to increase the thermal efficiency and to improve the conditions of turbine operation: superheat and reheat.

Superheated and reheated steam cycles

P1.1 Acknowledgements

Author: Antoine Veyrat-Masson, KTH, 2005; reviewed and modified by Catharina Erlich, KTH, 2005 and 2006

Author: Samuel Roy, KTH, 1998 Reviewer: Anders Nordstrand, KTH, 2005

Reviewer: Torsten Fransson, KTH; 1998, 2005

Reviewer: Marianne Salomon, KTH, 2005

Editor: Vitali Fedulov, KTH, 2005

P1.2 Literature

Moran M. J., Shapiro H. N., 1998; Fundamentals of engineering thermodynamics: SI version John Wiley & sons ltd, ISBN 0471979600

Rankine superheat and reheat cycles http://www.qrg.northwestern.edu/thermo/design-library/ Retrieved: 2005

Thermodynamics, parts 4.10 and 4.11 http://epic.mcmaster.ca/~garlandw/ep716/chap4.pdf

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Retrieved: 2005 Materials for Boilers in Ultra Supercritical Power Plants

http://asme.pinetec.com/ijpgc2000/data/html/15049.html Retrieved: 2005

Rankine based cycles http://www.eng.buffalo.edu/Courses/eas204/W04Ch09.pdf Retrieved: 2005

P1.3 Prerequisites

It is expected that the reader has the following background:

At least one year of engineering studies at university level, Basic thermodynamics (at least 160 LU = 4 weeks of fulltime studies), Basic steam cycle (S1B2C1).

P1.4 LU and TU

Learning Units: 3 Teaching Units: 1

P1.5 Thermal efficiency

The thermal efficiency of a power plant is the ratio between useful work obtained and energy rate of the fuel input.

S.2 Educational Objectives

At the end of the chapter the student should be able to:

Be familiar with the concept of steam quality at the turbine outlet, Identify the modifications of the basic steam cycle to build the superheat and reheat

cycles, Understand the influence of these modifications on work and efficiency, Analyze and perform calculations related to the superheat and reheat cycles.

3

S.3 Steam Quality at Steam Turbine Outlet

T

ssvaporssliquid

The quality of a vapor/liquid mixture is defined as mass-amount of vapor in the mixture i.e.:

10; <<+

= xmm

mx

liquidvapor

vapor

which can be expressed as:

liquidvapor

liquid

ssss

x−

−=

where s is entropy at the turbine outlet. In the basic steam cycle, when quality of

mixture passing through the turbine becomes too low, water droplets appear. The liquid droplets may cause erosion.

T-s diagram for a cycle working in the saturation area

P3.1 Quality

Entropy, s, is an extensive variable. Using other thermodynamic parameters, x can also be defined as:

liquidvapor

liquid

hhhh

x−

−= or

liquidvapor

liquid

vvvv

x−

−=

where v is specific volume, and h is enthalpy.

P3.2 Turbine

A steam turbine

source

4

P3.3 Liquid droplets may cause erosion

Water droplets do not follow the stream-lines of the gaseous fraction, because of the density difference. As a result they hit the rotating blades at high speed.

Once on the blade, the water droplets form a film which moves to the blade edge. Here the water is re-entrained into the steam flow in the form of new larger droplets. The larger droplets have stronger negative impact on the steam flow and the blades.

It is often considered unwise to allow steam with quality less than 85-90% within the turbine.

There are two ways of solving the problem with steam of low quality:

- To mechanically remove the condensate from the turbine: this can be done by sucking water from the turbine casing or from holes in the turbine blades. Unfortunately, as removing condensate from a moving turbine is not a trivial task, this option significantly complicates turbine design.

- To redesign the cycle so that steam at the turbine outlet has acceptable quality: this is where the reheat/superheat processes are applied.

Blade eroded with water

Source

S.4 Superheated Steam Cycle

The difference between a superheated steam cycle and the basic steam cycle is that in the superheated steam cycle the steam is brought to superheated state in the boiler.

Within the boiler, water is heated in the economizer, transformed into steam in the evaporator, and superheated in the superheater.

Three main boiler sections

5

The heating processes can be considered isobaric (under constant pressure). In reality there is a certain pressure drop due to hydraulic losses in the boiler.

Superheat raises the average temperature of heat supply. As a result, an improvement of cycle efficiency is achieved.

Another important factor is that steam will have higher quality after full expansion in the

turbine. This helps to increase turbine efficiency and to reduce the risk of erosion of turbine blades.

The superheat temperature is limited by boiler pipe material strength and the temperature of the primary heat source (burning fuel).

Analysis of the superheat cycle is similar to analysis of the basic steam cycle, except that

the steam after the boiler is superheated (and not saturated as in the basic cycle).

State diagram of superheated steam cycle

P4.1 Improvement of cycle efficiency

According to Carnot, the ideal cycle efficiency can be calculated as:

1

21TT

Carnot −=η

By increasing the average temperature at heat supply, T1, the cycle efficiency is improved.

In the Carnot cycle, the temperature of heat supply, per definition, is constant. In real

cycles, including the Rankine cycle, heat is supplied in non-constant temperature (in grows in the boiler). Nevertheless, the Carnot formula can be used for an ideal evaluation of cycle efficiency if T1 is the average temperature of heat supply in the boiler.

Comparing the superheat cycle and the basic cycle with saturated steam, the average

temperature of heat supply is higher in the superheat cycle.

P4.2 Boiler pipe material strength

The boiler piping material sets the upper limit on how high steam temperature/pressure can be achieved. Stainless steel manages steam temperatures well up to 600°C.

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For steam temperatures higher than 600°C other materials are required, which increases the boiler cost.

For example high strength ferritic 9-12Cr steels for use in thick section components are now commercially available for temperatures up to 620°C.

Advanced austenitic stainless steels for use as superheating tubing are available for steam temperatures up to 650°C and possibly 700°C.

Higher strength materials are needed for boilers with steam pressure above 240 bar. High-strength Chromium steel is possible to use for high-pressure boilers.

P4.3 Analysis of the superheat cycle is similar to analysis of the basic steam cycle

Example comparing saturated and superheated steam cycles not considering boiler efficiency or turbine efficiency Alternative 1 (a1): Water at 60 bar, 60°C and 50 kg/s is heated and vaporized to saturated steam. Thereafter the steam is expanded isentropically in a steam turbine to 0.2 bar. What is the cycle efficiency, assuming that pump work is neglected? Alternative 2 (a2): Water at 60 bar, 60°C and 50 kg/s is heated, vaporized and superheated to 500°C. Thereafter the steam is expanded isentropically in a steam turbine to 0.2 bar. What is the cycle efficiency, assuming that pump work is neglected? Solution (numbered subscripts according to the flow diagram on the main slide): In order to calculate the efficiency, the turbine power output and the heating rate in the boiler need to be determined. By estimating the enthalpies in the cycle, the power output and heating rate can be calculated. Enthalpy of feedwater in the boiler inlet h2 = 256.2 kJ/kg for both alternatives. Enthalpy of live steam is the same as in the turbine inlet: h3,a1 = saturated steam 60 bar = 2785 kJ/kg h3,a2 = steam at 60 bar and 500°C = 3425 kJ/kg Isentropic enthalpy in the turbine outlet is found from the h-s diagram, by drawing a straight vertical line (constant entropy=isentropic) from h3 to the pressure 0.2 bar. h4,a1 ≈ 1950 kJ/kg h4,a2 ≈ 2270 kJ/kg Power output from turbine P= m·(h3 – h4): PT, a1 = 50·(2785 – 1950) kW = 41 750 kW PT,a2 = 50·(3425 – 2270) kW = 57 750 kW Boiler heat flow input (Q = m·(h3 – h2)):

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kWQ aB 126440)2.2562785(501, =−⋅=&

kWQ aB 158440)2.2563425(502, =−⋅=& Cycle efficiency:

%0.33330.012644041750

1, →==acycleη

%4.36364.015844057750

2, →==acycleη

The efficiency increased because comparable more work was gained than the amount of heat needed to be added in the boiler.

P4.3.1 Live steam

Live steam is a common term for steam coming from a boiler at full pressure.

P4.3.2 h-s diagram

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S.5 Steam Cycle Combining Reheat and Superheat

The superheated steam cycle is commonly used in power generation. A modification of the superheated steam cycle, called reheat, gives additional

technological and economical benefits. Reheat is achieved by splitting the expansion phase into two (or more) sequential phases.

In-between, steam is returned to the boiler for reheating. This corresponds to dividing one turbine into two (or more) steps as shown in the figure below.

Steam cycle with reheat

Process diagram of steam cycle with reheat

Work output from the turbine is the sum of work from the separate turbines.

The boiler heating rate is the sum of heat provided for water heating, vaporization,

superheating and reheating.

Advantages of steam cycle with reheat are:

• improved cycle efficiency compared to the simple superheat cycle, • higher steam quality in the turbine outlet (due to steam entropy increased

during reheating).

Exemplary calculation analysis of superheated and reheated steam cycle

P5.1 Reheating

A reheater is a gas-to-gas heat exchanger in the boiler.

Reheat of steam can be considered isobaric (no considerable pressure drop in the reheater). This means that steam entering next turbine has the same pressure as it had in the outlet of the previous turbine.

A reheat cycle divides the turbine into de-facto 2-3 turbines, often indicated as high

pressure turbine (HP), intermediate pressure turbine (IP) and low pressure turbine (LP).

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It is not economically feasible to have more than 4 turbines (3 reheaters), because the efficiency increase becomes smaller for each new reheater added. Two separate turbines with a reheater are much more expensive than a single steam turbine.

In some power plants, steam from HP turbine is taken directly to IP/LP turbine without

reheat. The only reason to separate the expansion into two turbines in this case is to manage a large pressure decrease, and/or increase the power plant flexibility.

P5.2 Sum of work

Total specific work production [kJ/kg] including pumping work is:

( ) ( ) )( 1265432,1, hhhhhhwwww Ptt −−−+−=−+=

where wt,1 and wt,2 are corresponding work produced in turbine 1 and 2, and wp is feed-water pump work; hi are enthalpies corresponding to thermodynamic state i of the working fluid.

As pump work consumption is much less than work produced in the turbine, the total work can be approximated as:

( ) ( )6543 hhhhw −+−≈

P5.3 Boiler heating rate

Heat supplied in boiler

Specific heat input (kJ/kg) into the boiler includes the reheat:

( ) ( )4523 hhhhqB −+−=

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P5.4 Improved cycle efficiency

The cycle efficiency, neglecting the pump work is:

( ) ( )[ ]( ) ( )[ ]

B

BB

tt

hhhh

hhhhq

ww

ηη

η 1/4523

65432,1,

⋅−+−

−+−=

+=

The efficiency of reheat cycle is higher than for the simple superheat cycle, because the average temperature of heat supply is higher for the former.

This average temperature can be considered to be the mean between the temperature averages of 2 to 3 and of 4 to 5.

Even if the temperature in 5 is lower than in 3, there will be an efficiency increase as long as the average temperature of heating from 4 to 5 is higher than from 2 to 3.

P5.5 Exemplary analysis of superheated and reheated steam cycle

In this example, boiler efficiency and turbine efficiency are not considered. Water at 60 bar, 60°C and 50 kg/s is heated, vaporized and superheated to 500°C. This steam expands isentropically in a high pressure (HP) steam turbine to 10 bar. Thereafter the steam is brought back to the boiler and reheated under constant pressure to 500°C. A low pressure (LP) turbine expands this steam to 0.2 bar isentropically. What is the cycle efficiency neglecting the pump work? Solution In order to calculate the efficiency, the total turbine power output (sum of each turbine) and the total heating rate in the boiler need to be determined. By estimating the enthalpies in the cycle, the power output and heating rate can be calculated. Start with what is coming into the first turbine (HP). h3 = steam at 60 bar and 500°C = 3425 kJ/kg The enthalpy out from HP turbine (h4) is the same as that entering the reheater. This enthalpy is found from graph (h-s diagram), by drawing a straight vertical line (constant entropy=isentropic) from h3 to pressure 10 bar, which is the outlet pressure of HP turbine. h4 ≈ 2925 kJ/kg The power output in the HP turbine is thus : PT, HP = m·(h3 – h4) = 50·(3425 – 2925) kW = 25 000 kW The reheater brings the 10 bar steam to 500°C, thus the enthalpy out from reheater (=entering the LP turbine) is:

12

h5 = steam at 10 bar and 500°C = 3475 kJ/kg Expansion isentropically in the LP turbine from 10 bars, 500°C to 0.2 bar gives: h6 ≈ 2560 kJ/kg The power output in the LP turbine is thus: PT, LP = m·(h5 – h6) = 50·(3475 – 2560) kW = 45 750 kW The total power output is: PT = PT,HP + PT,LP = 25000 + 45750 kW = 70750 kW The heating rate in the boiler consists of heating, vaporization, superheating and reheating: QB = m·(h3 – h2) + m·(h5 – h4) Where enthalpy of feed water into boiler h2 = 256.2 kJ/kg QB = 50·(3425 – 256.2) + 50·(3475 –2925) kW = 185 940 kW

%0.38380.018594070750

, →==reheatcycleη

Comparing the efficiency of the reheat cycle and the efficiency from simple superheating in one step (earlier in this chapter), it is seen that the reheat-superheat combination increased the cycle efficiency further 1.6%, from 36.4% to 38.0%.

S.6 Summary

Superheat and reheat increase the thermal efficiency of a steam cycle. Superheated steam results in increased steam quality at the turbine outlet. Reheat also

contributes to the increased steam quality, eliminating the risk of water droplet erosion on the turbine blades.

In the reheat cycle, a set of turbines (high pressure, intermediate pressure and low pressure) are used in combination with several reheat steps.

Another way to increase the cycle efficiency and the net work produced are the regenerative cycles, studied in the next chapter.

This you must know

P6.1 This you must know

Definition of steam quality and how to calculate it from different parameters. The relation between steam quality and steam turbine erosion. Explain how superheated steam affects the steam cycle efficiency compared to the

basic cycle with saturated steam. Analyze a steam cycle with superheated steam. Explain how reheat affects the steam cycle efficiency. Analyze a steam cycle with superheated steam that is reheated.

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P6.2 Quiz

Liquid droplets in the steam turbine are… • Necessary to push turbine blades and create a

momentum

• Increasing the thermal efficiency • Damaging the blades Correct

answer

Superheat cycle… • Increases the amount of moisture in the turbine • Has better efficiency than the basic Rankine cycle Correct

answer • Increases temperature in the condenser • Increases the temperature in the pump to reduce its

work input

With typical materials used today, temperature of live steam is about… • 300°C (572°F) • 900°C (1652°F) • 100°C (212°F) • 600°C (1112°F) Correct

answer

Thermal efficiency for a cycle is defined as…

• T

PT

WWW −

=η

•

P

T

WW

=η

•

B

PT

QWW −

=η Correct answer

•

B

TP

QWW −

=η

Thermal efficiency of a steam cycle is… • Negative • between 0 and 1 Correct

answer • between 0% and 100% Correct

answer

The unit of thermal efficiency is… • kW/kg • dimensionless Correct

answer • kJ/kg • kW

In the reheat cycle, which additional component is added compared with the basic Rankine

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cycle? • A turbine Correct

answer • A condenser • A pump • They have exactly the same number of components

In the boiler, the fluid is heated… • Adiabatically • Isentropically • At constant pressure Correct

answer • At constant temperature

The reheat cycle work is defined as… • W = Wt,1 + Wt, 2- WP Correct

answer • W = Wt,1 + Wt,2 + WP

• P

tt

WWW

W 2,1, +=

• W = Wt,1 - Wt,2 - WP