Steam Cycle notes

Thermodynamics - Semester 1 2013 - Lecture Notes

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Chapter 8 Steam Cycle Analysis

� Thermodynamic cycles in internal combustion engines, e.g. gas turbines, spark-ignition engines,

and diesel engines, are usually called gas power cycles because the working fluid remains in

the gaseous phase throughout the entire cycle.

� Thermodynamics cycles involving phase change of the working fluid are called vapor cycles.

Steam turbines use liquid water and steam to produce power and are called vapor power cycles.

Refrigeration cycles (discussed in Chapter 9) move heat from low temperature medium to high-

temperature medium involving phase change of the refrigerant and are called vapor

refrigeration cycles.

8.1 Phase Change of Pure Substances

8.1.1 States of liquid and vapor

• A liquid that is about to vaporize is called saturated liquid (state 2 in the figure below). A vapor that is about to condense is called saturated vapor (state 4 below). A state between 2 and 4 is called saturated liquid-vapor mixture (state 3).

Water


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• Away from the saturation line, a liquid that is not about to vaporize is called compressed liquid. A vapor that is not about to condense is called superheated vapor.

• At a given pressure, the temperature at which a pure substance changes phase is called the saturation temperature Tsat. At a given temperature, the pressure at which a pure substance changes phase is called saturation pressure Psat.

� The energy absorbed or released during a phase-change process is called latent heat. For

phase change between liquid and vapor, it is called latent heat of vaporization. Ethalpy of

vaporization of water at 1 atm is 2256.5 kJ/kg.

8.1.2 Property diagrams for phase-change processes

� Tsat and Psat depend on each other. Higher Tsat occurs at higher Psat, and vice versa. This is why

water boils at < 100°C at higher elevation.

� On the T-v diagram, the saturation lines move up at higher pressures but shrink in length and

become a point at the critical point.

� Above the critical point, there is no distinctive phase change process.

� The saturated liquid points on the T-v diagram can be connected together and the resulted line

is called saturated liquid line. Similarly, saturated vapor line can be defined.


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8.1.3 Property tables

• The ideal gas law only describes gases that are well removed from any phase change boundary. It is therefore completely incorrect to use the ideal gas equation for mixtures of liquid & vapour and for any gas near a phase change boundary.

• Therefore, property tables and charts should be used instead.

Water


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Saturated liquids and vapors

• Properties of saturated liquid and saturated vapour can be respectively found from thermodynamic tables and charts.

• To determine thermodynamic properties for saturated mixtures underneath the saturation lines, a property of steam “quality” x is defined as the ratio of the mass of vapour to the total mass of the mixture:

g

f g

mxm m

=+

0 < x < 1

where gm and fm are the mass of saturated vapour and saturated liquid, respectively.

• The specific entropy s ( /J kgK ) is then:

( )fg

f g f

s

s s x s s= + −��

• The specific enthalpy h ( /J kg ) is:

( )fg

f g f

h

h h x h h= + −��

• The specific volume v ( 3 /m kg ) is:

( )fg

f g f

v

v v x v v= + −��

where the subscripts fg refers to the difference between the saturated liquid and vapour.


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Superheated vapor and compressor water

• Properties of superheated vapors are also tabulated (note that the ideal-gas law is not applicable). In this case, the pressure and temperature no longer depend on each other, but are two independent properties.

• Properties of compressed liquid are not usually tabulated (except for water), because properties of condensed matter are nearly independent of pressure.

• Based on the State Postulate that a state of a simple system can be completely specified by two independent intensive properties, knowing any two properties will let us know all the other properties for that state from the property tables. Note that during phase change, the temperature and pressure are not independent. For this case, the steam quality “x” (an intensive property) is used to define the state of the saturated mixtures, x = 0 for saturated liquid and x = 1 for saturated vapor.

• The State Postulate plus the property tables is the primary tool for solving vapor-cycle problems (for both steam cycles and refrigeration cycles analysis).

8.2 Rankine cycle

• Steam power plants produce most of the electricity in the world. The steam power cycle can be approximated by the ideal Rankine cycle. The schematic and T-s diagram are shown below.


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8.2.1 Rankine cycle analysis

• Process 1-2: isentropic compression (q = 0), the pump work input equals

2 1pw h h= −

• From the Gibbs equation

2

2 1

1

0Tds dh vdp

dh vdp

h h vdp

= − =

⇒ =

∴ − = ∫

• since v is approximately constant for a liquid:

2 1 1 2 1( )pw h h v p p= − = −

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


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• Since the specific volume of liquid water is very small, this pump work is small compared to other terms in the energy equation.

• Process 2-3: constant pressure heat addition (w = 0) in a boiler where the compressed water is heated to superheated steam. The heat addition of the cycle is

3 2inq h h= −

• Process 3-4: isentropic expansion (q = 0). The turbine work is

4 3tw h h= −

Note that the state 4 in the shown figure is a saturated mixture where the steam quality needs to be known. The state 4 can also be saturated vapor or superheated vapor as well.

• Process 4-1: constant pressure heat rejection (w = 0) in a condenser. The heat rejection is

4 1outq h h= −

• The energy balance of the cycle can be written as

p in t outw q w q+ = + or t p in outw w q q− = −

• The thermal efficiency of the cycle can be obtained as

1t pnet out

th

in in in

w ww q

q q qη

−= = = −


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• Note that the isentropic efficiency of the turbine and the pump can be defined similarly to those in the gas turbine analysis.

3 4

3 4

actual work

isentropic work

a at

s s

w h h

w h hη

−≡ = ≅

−

2 1

2 1

isentropic work

actual works s

p

a a

w h h

w h hη

−≡ = ≅

−

8.2.2 Improve Rankine cycle efficiency

• Efficiency of the Rankine cycle can be improved by varying the operating temperature and pressure. Higher efficiency can be achieved by increasing the average temperature at which heat is added to the working fluid (Principle 1), or by decreasing the average temperature at which heat is removed from the working fluid (Principle 2). This is directly related to the Carnot efficiency for heat engines

1 Lcarnot

H

T

Tη = −


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Lowering condenser pressure

• Lowering the condenser pressure reduces the average temperature when the heat is removed from the working fluid (Principle 2 in the above). The increased cycle work is shown in the shaded area in the figure below.

• This approach is limited by the temperature of the cooling medium (typically rivers, lakes, or ambient air) that takes away the condensation heat from the condenser.

• Potential problems are with this method. 1) Low condenser pressure increases the possibility for air leak as practical condensers already operate at highly vacuum pressures. 2) More moisture is resulted in the steam at the final stage of the turbine. High moisture content is highly undesirable in turbine because it decreases the turbine efficiency and erodes the turbine blades.

Lowering condenser pressure superheating steam increasing boiler pressure


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Superheating steam

• Superheating steam increases the average temperature at which heat is added to the working fluid (Principle 1).

• The approach also reduces the steam moisture content at the turbine exit which is very desirable. This approach, however, is limited by the maximum temperature that the turbine blades can withstand, which presently is 620°C.

Increasing boiler pressure

• Increasing the boiler pressure increases the average temperature at which heat is added to the working fluid (Principle 1). Modern steam turbines can operate at pressure as high as 30 MPa.

• With the maximum cycle temperature is limited, this approach however increases the moisture content in the turbine. This problem can be corrected by reheating discussed below.

8.2.3 Ideal reheated Rankine cycle

• The problem of high moisture-content at the turbine exit can be effectively solved by using two-stage turbines and reheating the steam (in the boiler) between the high-pressure and low-pressure turbines.


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• The total heat input and work output for the cycle can be written as

( ) ( )( )

3 2 5 4

, , 3 4 5 6 2 1( ) ( )

in primary reheat

net turb hp turb lp p

q q q h h h h

w w w w h h h h v p p

= + = − + −

= + − = − + − − −

• The reheat temperature (T5) is very close or equal to the turbine inlet temperature (T3). The optimal reheat pressure (p5) is about 1/4 of the maximum cycle pressure (p3).


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8.2.4 Ideal regenerative Rankine cycle

• Another widely used Rankine cycle involves bleeding a portion of the steam during turbine expansion to heat the compressed feedwater exiting the pump. The device where the feedwater is heated by steam is called a regenerator or a feedwater heater (FWH).

• Regeneration improves the cycle efficiency by reducing the energy required to heat the compressed water, even though the net work output is reduced.

• In addition to the higher efficiency, regeneration provides a convenient means of deaerating the feedwater (removing the air leaked in at the condenser) to prevent corrosion in the boiler. It also helps to control the large volume-flow-rate of the steam at the final stages of the turbine. Regeneration is used in all modern steam power plants.

• Heat transfer between the feedwater and the steam can occur either by mixing the two streams (open FWH) and using a heat exchanger (closed FWH).

Open feedwater heater

• An open FWH is basically a mixing chamber, where the steam extracted from the turbine mixes with the feedwater (compressed liquid) exiting the pump. Ideally, the mixture leaves the heater as a saturated liquid at the heater pressure.

• Assuming out of 1 kg of total steam in the cycle, y kg is extracted from the turbine to the FWH, the energy balance for the shown cycle with single open FWH is:

Input

Output

5 4

7 1(1 )( )

in

out

q h h

q y h h

= −

= − −

( )( )

2 1 4 3 1 2 1 3 4 3

5 6 6 7

(1 ) ( ) (1 ) ( ) ( )

(1 )( )

p

t

w y h h h h y v p p v p p

w h h y h h

= − − + − = − − + −

= − + − −


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Closed feedwater heater

• In a closed FWH, the heat transfer between the steam and the feedwater occurs in a heat exchanger. The two streams can be at different pressure since they do not mix.

• In the ideal case, the steam leaves the heater as a saturated liquid at the extraction pressure. The condensed steam can be then pumped to the feedwater pressure and mixed together.

• The energy balance for a closed FWH cycle can be analyzed in an identical manner to that in the open FWH cycle.


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• Compared to a closed FWH, an open FWH is simpler, less expensive, and more effective, but requires dedicated pump for each heater when multiple heaters are used (which is common in practice). Most steam plants use a combination of open and closed FWHs.

8.3 Cogeneration and Combined Power Cycles

• Steam power cycles can be combined with other industrial processes to substantially improve the overall energy utilization effectiveness.


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• Cogeneration is to combine steam power generation with process heating. Combined cycle is to combine gas power generation with steam power generation.

8.3,1 Cogeneration

• In a steam power cycle, the low-temperature (low-grade) thermal energy in the steam exiting the turbine can be potentially used as process heat. Process heat is required by certain industries, such as chemical plant, oil refineries, food processing, etc.

• Process heat in these industries is usually supplied by steam at 5 – 7 atm and 150 – 200°C from burning fuels in furnaces.

• A cogeneration plant with adjustable loads is shown in the right figure. Under normal conditions, some steam is extracted from the turbine at some predetermined intermediate pressure. The rest of the steam expands to the condenser pressure and is then cooled at constant pressure.

• When the demand of process heat is high, all the steam is routed to the process heating unit and none to the condenser. The waste heat is zero in this mode. If this is not sufficient, some steam leaving the boiler is throttled to the extraction pressure and is directed to the process-heating unit.

• When there is no demand of process heat, all the steam passes through the turbine and condenser, and the cogeneration plant operates as an ordinary steam power plant.


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• A cogeneration plant can reach very high utilization factor (as defined below), ε > 0.8, due to the small fraction of waste heat.

net work output + process heat delivered

total heat input

1net p out

in in

W Q Q

Q Q

ε =

+= = −

ɺɺ ɺ

ɺ ɺ

Note the utilization factor is different from the thermal efficiency.

8.3.2 Combined gas-vapor power cycles

• Gas turbine power cycles operate at much higher temperatures than steam power cycles. For example, the turbine inlet temperatures are > 1400°C and ~ 620°C, respectively, for the two cycles.

• The gas temperatures at the exit of gas turbines are usually above 500°C, which can be potentially used to heat the steam in the steam cycles. The combined gas-vapor power cycle can significantly improve the thermal efficiency for power generation.

• As shown in the figure below, the energy is recovered from the exhaust gases by transferring it to the steam in a heat exchanger that serves as the boiler. More than one gas turbine is usually needed to supply sufficient heat to the steam.

• The combined gas-vapor cycles have been implemented in many existing and new power plants and thermal efficiencies as high as 60% have been reported. These efficiencies are substantially higher than that can be achieved by any individual heat engines in practice.


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Steam Cycle notes

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