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Combustion and Power GenerationGas and Steam Cycles, Steam Turbines

Conversion of Thermal Energy• Thermodynamic Power Cycles• Internal-Combustion Engines

and Engine Cycles• Engine Performance

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• External-Combustion Systems• Vapor-Power Cycles• Combined Cycles

Steam Turbines

Conversion of Thermal Energy• Almost all of the mechanical energy produced today

is produced from the conversion of thermal energy in some sort of heat engine.

• The operation of all heat-engine cycles can usually be approximated by an ideal thermodynamic power cycle of some kind.

• A basic understanding of these cycles can often show the power engineer how to improve the operation and performance of the system.

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Thermodynamic Power CyclesThermodynamic Power Cycles

• For a thermodynamic heat-engine cycle, the figure of merit is called the thermal efficiency, or ηth. The desired energy output is the net work output of the cycle and the energy that costs is the heat addedcycle and the energy that costs is the heat added from the high-temperature heat sources.

• Another important parameter of any heat-engine cycle is the specific work, w, which is the net work output per pound of working fluid in the cycle. It is also equal to the area enclosed by the cycle diagram

hen it is plotted on either a P or T s diagram

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when it is plotted on either a P-v or T-s diagram, providing the mass flow rate of the working fluid is the same throughout the cycle and the processes are reversible.

P-υ and T-s Diagrams of Power CyclesThe area under the heat addition process on a T-sdiagram is a geometric measure of the total heat supplied during the cycle qin, and the area under the heat rejection process is a measure of the total heat rejected qout. The difference between these two (the area enclosed by the cyclic curve) is the net heat transfer, which is also the net work produced during the cycle.

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Reversible Heat-Engine CyclesReversible Heat-Engine Cycles• The second law of thermodynamics states that it is

impossible to construct a heat engine or to develop a power cycle that has a thermal efficiency of 100%. This means that at least part of the thermal energymeans that at least part of the thermal energy transferred to a power cycle must be transferred to a low-temperature sink.

• There are four phenomena that render any thermodynamic process irreversible. They are:

Friction

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Unrestrained expansionMixing of different substancesTransfer of heat across a finite temperature difference

• Thermodynamic cycles can be divided into two general categories: Power cycles and refrigerationcycles.

• Thermodynamic cycles can also be categorized as

Categorize Cycles

• Thermodynamic cycles can also be categorized as gas cycles or vapor cycles, depending upon the phase of the working fluid.

• Thermodynamic cycles can be categorized yet another way: closed and open cycles.

• Heat engines are categorized as internal or external

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g gcombustion engines.

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Air-Standard AssumptionsTo reduce the analysis of an actual gas power cycle to a

manageable level, we utilize the following approximations, commonly know as the air-standard assumptions:p

1. The working fluid is air, which continuously circulates in a closed loop and always behaves as an ideal gas.

2. All the processes that make up the cycle are internally reversible.

3. The combustion process is replaced by a heat-addition

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p p yprocess from an external source.

4. The exhaust process is replaced by a heat rejection process that restores the working fluid to its initial state.

Air-Standard CycleAnother assumption that is often utilized to simplify the analysis even more is that the air has constant specific heats whose values are determined at room temperature (25oC, or 77oF). When this assumption is utilized, the air-standard assumptions are called the cold-air-standard assumptions. A cycle for which the air-standard assumptions are applicable is frequently referred to as an air-standard cycle.

The air-standard assumptions stated above provide considerable simplification in the analysis without

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considerable simplification in the analysis without significantly deviating from the actual cycles.

The simplified model enables us to study qualitatively the influence of major parameters on the performance of the actual engines.

5

Mean Effective PressureThe ratio of the maximum volume formed in the cylinder to the minimum (clearance) volume is called the compression ratio of the engine.

TDC

BDC

min

maxVV

VVr ==

Notice that the compression ratio is a volume ratio and should not be confused with the pressure ratio.

Mean effective pressure (MEP) is a fictitious pressure that, if it acted on th i t d i th ti

TDCmin VV

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the piston during the entire power stroke, would produce the same amount of net work as that produced during the actual cycle.

minmax

netVV

WMEP−

=

Three Ideal Power CyclesThree Ideal Power Cycles• Three ideal power cycles are completely reversible

power cycles, called externally reversible power cycles. These three ideal cycles are the Carnot cycle, the Ericsson cycle, and the Stirling Cycle.y , g y

10

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Three Ideal Power CyclesThree Ideal Power Cycles• The Carnot cycle is an externally reversible power cycle

and is sometimes referred to as the optimum power cyclein thermodynamic textbooks. It is composed of two reversible isothermal processes and two reversiblereversible isothermal processes and two reversible adiabatic (isentropic) processes.

• The Ericsson power cycle is another heat-engine cycle that is completely reversible or “externally reversible.” It is composed of two reversible isothermal processes and two reversible isobaric processes (with regenerator).

• The Stirling cycle is also an externally reversible heat-

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g y yengine cycle and is the only one of the three ideal power cycles that has seen considerable practical application. It is composed of two reversible isothermal processes and two reversible isometric (constant volume) processes.

Carnot Cycle and Its Value in Engineering

The Carnot cycle is composed of four totally reversible processes: isothermal heat addition isentropic expansionaddition, isentropic expansion, isothermal heat rejection, and isentropic compression (as shown in the P-υ diagram at right). The Carnot cycle can be executed in a closed system (a piston-cylinder device) or a

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p y )steady-flow system (utilizing two turbines and two compressors), and either a gas or vapor can be used as the working fluid.

H

LCarnot,th T

T−=1η

7

Limit of TH and TL in a Carnot CycleThermal efficiency increases with an increase in the average temperature at which heat is supplied to the system or with a decrease in the average temperature at which heat is rejected from the system.

The highest temperature in the cycle is limited by the maximum temperature that the components of the heat engine, such as the piston or turbine blades, can withstand. Th l t t t i

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The lowest temperature is limited by the temperature of the cooling medium utilized in the cycle such as a lake, a river, or atmospheric air.

Internal-Combustion Engine CyclesInternal-Combustion Engine Cycles• Internal-combustion (IC) engines cannot operate on an ideal reversible heat-engine cycle but they can be approximated by internally reversible cycles in which all the processes are reversible except the heat-

• Internal-combustion (IC) engines cannot operate on an ideal reversible heat-engine cycle but they can be approximated by internally reversible cycles in which all the processes are reversible except the heat-all the processes are reversible except the heataddition and heat-rejection processes. all the processes are reversible except the heataddition and heat-rejection processes. • In general, IC engines are more polluting than

external-combustion (EC) engines because of the formation of nitrogen oxides, carbon dioxide, and unburned hydrocarbons.

• The Otto cycle is the basic thermodynamic power

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The Otto cycle is the basic thermodynamic power cycle for the spark-ignition (SI), internal-combustion engine.

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Otto Cycle: The ideal Cycle for Spark-Ignition EnginesFigures below show the actual and ideal cycles in spark-ignition (SI) engines and their P-υ diagrams.

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Ideal Otto CycleThe thermodynamic analysis of the actual four-stroke or two-stroke cycles can be simplified significantly if the air-standard g yassumptions are utilized. The T-sdiagram of the Otto cycle is given in the figure at left.

The ideal Otto cycle consists of four internally reversible processes:

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1→2 Isentropic compression2→3 Constant volume heat addition3→4 Isentropic expansion4→1 Constant volume heat rejection

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Thermal Efficiency of an Otto CycleThe Otto cycle is executed in a closed system, and disregarding the changes in kinetic and potential energies, we have( ) ( ) =−+− outinoutin uwwqq ∆( ) ( )

( )( )

( )( ) 1

1141

23

14

1414

2323

11111

11

−=−=−

−=

−−

−=−==

−=−=⇒−=−=⇒

k

in

out

in

netOtto,th

vout

vin

outinoutin

TT/TTTTTT

qq

qw

TTCuuqTTCuuq

qq

η

17

( ) 12232 1 −− krTT/TT

2

1

2

1

3

41

4

31

1

2

2

1υυ

υυ

υυ

====

=

=

−−

VV

VVr

TT

TT

min

maxkk

and; Where,

Engine Knock and thermal Efficiency of an EngineThe thermal efficiency of the ideal Otto cycle increases with both the compression ratio and the specific heat ratio.

When high compression ratiosWhen high compression ratiosare used, the temperature of the air-fuel mixture rises above the autoignition temperature produces an audible noise, which is called engine knock. (antiknock, tetraethyl lead? →

18

( yunleaded gas)

For a given compression ratio, an ideal Otto cycle using a monatomic gas (such as argon or helium, k = 1.667) as the working fluid will have the highest thermal efficiency.

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Example IV-4.1: The Ideal Otto CycleAn ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, the air is at 100 kPa and 17oC, and 800 kJ/kg of heat is t f d t i d i th t t

determine a) the maximum temperature and pressure that occur during the cycle, b) the net work output, c) the thermal efficienc and d) the mean effecti e press re for

transferred to air during the constant-volume heat-addition process. Accounting for the variation of specific heats of air with temperature,

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thermal efficiency, and d) the mean effective pressure for the cycle. <Answers: a) 1575.1 K, 4.345 MPa, b) 418.17 kJ/kg, c) 52.3%, d) 574.4 kPa>

Solution:

( )

,

:gas) ideal an of ncompressioc (isentropi 2-1 Process ,

:cycle Otto an in pressure and etemperatur Maximum

rr

r

r

kg/kJ.uK.T..vvvv

.vkg/kJ.uKTa

11475465251848

16761

167691206290

221

222

111

==⇒===⇒==

==⇒=

:addition) heat volume (constant 3-2 Process

inin

r

vTvPvP

K.Tkg/kJ..uquuuq

kPa..vv

TTPP

TvP

TvP

rrvv

11575

1157511127511475800

717998290

4652100

8

32323

2

1

1

212

1

11

2

22

11

=⇒=+=+=⇒−=

=××=

=⇒=

20volume.specific property the withconfused be not should and processes, isentropic of analysis the in usedquantity

essdimensionl a is volume)specific (relative property The rv:Note

MPa...MPa.

vv

TTPP

TvP

TvP 34541

4652115757971

3

2

2

323

2

22

3

33 =××=

=⇒=

11

( )

,

:gas) ideal an of expansionc (isentropi 4-3 Process:output worknet The

745886795

8644810868

44

343

4

3

4

kg/kJ.uK.T

..rvvrvv

vv

b

rrr

r

==⇒

=×==⇒==

( )

( )52.3%or

:efficiency thermal The Thus,

:rejection) heat volume (constant 1-4 Process ,

523017418

1741883381800833819120674588

745886795

1441

44

..wc

kg/kJ..qqqwkg/kJ...uuquuq

kg/kJ.uK.T

netth

outinnetnet

outout

===

=−=−===−=−=⇒−=−

⇒

η

21

( )

( ) ( )

s.assumption this utlizing in exercised be should Care

56.5% or

:sassumption standard-air-cold the Under

52.3%or

565081111

5230800

41111 .r

r

.q

.kkth

inth

=−=−=−= −−−η

η

( ) :definition its from determined is pressure effective mean The

kgm.

kPa

KK.kgm.kPa.

PRTv

d

8320100

2902870 3

3

1

11

=×

==

cycle. entire the as output worknet same the produce wouldstroke power the during kPa 574.4 of pressure constant a Therefore,

Thus, netnet kPa.kJ

m.kPa..

.

rvv

wvv

wmep 45741

1

883208320

17418 3

11

21=

−=

−=

−=

22

e).temperatur room (at , heatsspecific constant given with #17Slideon shown equations usingby solved be could problem this that

vp ccNote

12

( ) ( )

( ) ( ) 4178026667180800

818378290

2666100

26668290

2

1

1

212

2

22

1

11

2411

2

11

1

2

2

1

KTTTTcq

kPa..vv

TTPP

TvP

TvPR

K.TT

rvv

TTa .k

k

⇒×

=×

×=

=⇒==

=⇒=⇒=

= −−

−

( ) ( )

( )

( ) ( ) 7745129007757180800

9114126664178081837

0775841780

4178026667180800

3

2

2

323

3

33

2

22

4141

4

1

2

11

3

4

4

3

3323

k/kJb

MPa....

vv

TTPP

TvP

TvPR

K.TT

.vv

vv

TT

K.T.T.TTcq

.kk

vin

=×

×=

=⇒==

=⇒=⇒

=

=

=⇒−×=−==

−−−

23

( ) ( )

( ) 56.5%) (or 5650800

774517745129007757180800

..qwc

kg/kJ...qqwb

in

netth

outinnet

===

=−×−=−=

η

Diesel Cycle: The Ideal Cycle for Compression-Ignition Engines

The diesel cycle is the ideal cycle for CI (Compression-Ignition) reciprocating engines. The CI engine first proposed by Rudolph Diesel in the 1890s, is very similar to the SI engine, differing mainly in the method of initiating combustion. In SI engines (also known as gasoline engines), the air-fuel mixture is compressed to a temperature that is below the autoignition temperature of the fuel, and the combustion process is initiated by firing a spark plug. In CI engines (also known as diesel engines), the air is compressed to a temperature that is b th t i iti t t f th f l d

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above the autoignition temperature of the fuel, and combustion starts on contact as the fuel is injected into this hot air. Therefore, the spark plug and carburetor are replaced by a fuel injector in diesel engines.

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Ideal Cycle for CI Engines (continued)

In diesel engines, ONLY air is compressed during the compression stroke, eliminating the possibility of autoignition. Therefore, diesel engines can be designed to operate at much higher compression ratios typicallyto operate at much higher compression ratios, typically between 12 and 24.

The fuel injection process in diesel engines starts when the piston approaches TDC and continues during the first part of the power stroke. Therefore, the combustion process in these engines takes place over a longer inter al Beca se of this longer d ration the comb stion

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interval. Because of this longer duration, the combustion process in the ideal Diesel cycle is approximated as a constant-pressure heat-addition process. In fact, this is the ONLY process where the Otto and the Diesel cycles differ.

Ideal Cycle for CI Engines (continued)

( )( )

( ) ( )

−

−=−

−=−==

−=−=

−=−=⇒−=−

11111 14

1414

232323

kc

koutnet

Dieselth

vout

pinout,bin

rTTqw

TTCuuq

TTChhquuwq

η ( ) ( )

−− − 1

111 123 c

kinin

Diesel,th rkrTTkqqη

2

1υυ

=r

Where,

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2

3υυ

=cr

and

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Thermal efficiency of Ideal Diesel CycleUnder the cold-air-standard assumptions, the efficiency of a Diesel cycle differs from the efficiency of Otto cycle by the quantity in the brackets. (See Slide #26)

Th tit i thThe quantity in the brackets is always greater than 1. Therefore, ηth,Otto > ηth, Diesel when both cycles operate on the same compression ratio.

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Also the cuttoff ratio, rcdecreases, the efficiency of the Diesel cycle increases. (See figure at right)

Internal-Combustion Engines

The two basic types of ignition or firing systems are the four-stroke-cycle engines, commonly called four-cycle engines, and the two-stroke-cycle engines, commonly called two-cycle enginescalled two-cycle engines.

The four-cycle engines has a number of advantages over the usual two-cycle engine, including better fuel economy, better lubrication, and easier cooling.

The two-cycle engine has a number of advantages, including fewer moving parts, lighter weight, and

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g g p , g g ,smoother operation. Some two-cycle engines have valves and separate lubrication systems.

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Cylinder Arrangements for Reciprocating Engines

Figure below shows schematic diagrams of some of the different cylinder arrangements for reciprocating engines.

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• Vertical in-line engine is commonly used today in four-and six-cylinder automobile engines.

• The V-engine is commonly employed in eight-cylinder (V-8) and some six-cylinder (V-6) automobile engines.

• The horizontal engine is essentially a V-engine with 180o between the opposed cylinders. This system was used as the four-cylinder, air-cooled engine that powered the Volkswagon “bug”.

• The opposed-piston engine consists of two pistons, two crankshafts and one cylinder The two crankshafts

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two crankshafts, and one cylinder. The two crankshafts are geared together to assure synchronization. These opposed-piston systems are often employed in large diesel engines.

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• The delta engine is composed of three opposed-piston cylinders connected in a delta arrangement. These systems have found application in the petroleum industry.

• The radial engine is composed of a ring of c linders in• The radial engine is composed of a ring of cylinders in one plane. One piston rod, the “master” rod, is connected to the single crank on the crankshaft and all the other piston rods are connected to the master rod. Radial engines have a high power-to-weight ratio and were commonly employed in large aircraft before the advent of the turbojet engine

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advent of the turbojet engine.

• When the term “rotary engine” is used today, it implies something other than a radial engine with a stationary crank.

Engine Performance

There are several performance factors that are common to all engines and prime movers. One of the main operating parameters of interest is the actual output of the engine The brake horsepower (Bhp) is the powerthe engine. The brake horsepower (Bhp) is the power delivered to the driveshaft dynamometer.

The brake horsepower is usually measured by determining the reaction force on the dynamometer and using the following equation:

2 FRNBhp dπ=

32

00033,Bhp =

Where F is the net reaction force of the dynamometer, in lbf, R is the radius arm, in ft, and Nd is the angular velocity of the dynamometer, in rpm.

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HorsepowerFor a particular engine, the relationship between the mean effective pressure (mep) and the power is:

( )( )( )pdis NVmepBhp =

00033

( ) ( )

minuteperstrokespowerofnumbertheisand

where

π

e

dis

minmax

net

CNN

strokeboreV

VVWmep

,p

=

=

−=

4

00033

2

33

minute.perstrokespowerofnumberthe is andζpN =

Where C is the number of cylinders in the engine, Ne is the rpm of the engine, and ζ is equal to 1 for a two-stroke-cycle engine and 2 for a four-stroke-cycle engine.

Brake Thermal Efficiency

The brake thermal efficiency of an engine, ηth, unlike power plants, is usually based on the lower heating value (LHV) of the fuel. The relationship between efficiency and the brake specific fuel consumption (Bsfc) y p p ( )is:

( )( )

( )Bhp

Bsfc

LHVBsfcth

lbm/h rate, fuel where

=

=2545η

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Note that the brake specific fuel consumption (Bsfc) of an engine is a measure of the fuel economy and is normally expressed in units of mass of fuel consumed per unit energy output.

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External-Combustion Systems

External-combustion power systems have several advantages over internal-combustion systems. In general, they are less polluting. The primary pollutants from internal-combustion engines are unburned ghydrocarbons, carbon monoxide, and oxides of nitrogen.

In external-combustion engines, the CHx and CO can be drastically reduced by carrying out the combustion with excess air and the NOx production can be markedly reduced by lowering the combustion temperature. By burning the fuel with excess air more energy is released

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burning the fuel with excess air, more energy is released per pound of fuel.

There are three general ideal external-combustion engine cycles, the Stirling and Brayton are ideal gas-power, and vapor power cycles.

The Brayton cycle was first proposed by George Brayton for use in the reciprocating oil-burning engine that he d l d d 1870

Brayton Cycle:The Ideal Cycle for Gas-Turbine Engines

developed around 1870.Fresh air at ambient conditions is drawn into the compressor, where its temperature and pressure are raised. The high-pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure. The resulting high-

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p g gtemperature gases then enter the turbine, where they expand to the atmospheric pressure, thus producing power. (An open cycle.)

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Brayton Cycle (continued)

The open gas-turbine cycle can be modeled as a closed cycle, as shown in the figure below, by utilizing the air-standard assumptions.The ideal cycle that the workingThe ideal cycle that the working fluid undergoes in this closed loop is the Brayton cycle, which is made up of four internally reversible processes:1→2 Isentropic compression (in a

compressor)

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2→3 Constant pressure heat addition

3→4 Isentropic expansion (in a turbine)

4→1 Constant pressure heat rejection

T-s Diagram of Ideal Brayton Cycle

Notice that all four processes of the Brayton cycle are executed in steady-flow devices (as shown in the figure ( gon the previous slide, T-sdiagram at the right), and the energy balance for the ideal Brayton cycle can be expressed, on a unit-mass basis, as

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( ) ( )( )

( )1414

2323

TTChhq

TTChhqhhwwqq

pout

pin

inletexitoutinoutin

−=−=

−=−=−=−+−

and

where

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P-υ Diagram and ηth of Ideal Brayton CycleThen the thermal efficiency of the ideal Brayton cycle under the cold-air-standard assumptions becomes

( )( )

( )( )p

p

in

out

in

netBrayton,th

T/TTT/TT

TTCTTC

qq

qw

232

141

23

14

11

1111

1

=

−−

−=−

−−=

−==η

39

( ) k/kpr 11 −−=

( ) ( )ratio. pressure the is and , where

1

2

4

31

4

31

1

2

1

2PPr

TT

PP

PP

TT

p

k/kk/k

==

=

=

−−

Thermal Efficiency of the Ideal Brayton Cycle

Under the cold-air-standard assumptions, the thermal efficiency of an ideal Brayton cycle increases with both the yspecific heat ratio of the working fluid (if different from air) and its pressure ratio (as shown in the figure at right) of the isentropic compression process.

The highest temperature in the cycle occurs at the end

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The highest temperature in the cycle occurs at the end of the combustion process, and it is limited by the maximum temperature that the turbine blades can withstand. This also limits the pressure ratios that can be used in the cycle.

21

Net Work of the Brayton Cycle

For a fixed turbine inlet temperature T3, the net work output per cycle increases with the pressure ratio, p ,reaches a maximum, and then starts to decrease, as shown in the figure at right. Therefore, there should be a compromise between the pressure ratio and the net work output In most

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work output. In most common designs, the pressure ratio of gas turbines ranges from about 11 to 16.

The Back Work RatioA power plant with a high back work ratio requires a larger turbine to provide the additional

i t fpower requirements of the compressor. Therefore, the turbine used in gas-turbine power plants are larger than those used in steam power plants of

In gas-turbine power plants, the ratio of the compressor work to the turbine work, called the back work ratio, is very high. Usually more than half of the

42

The two major application areas of gas-turbine engines are aircraft propulsion and electric power generation.

p pthe same net power output.

yturbine work output is used to drive the compressor.

22

Development of Gas TurbinesThe efforts to improve the cycle efficiency concentrated

in three areas:1. Increasing the turbine inlet (or firing) temperature

(high NOx!?) which can be achieve by the d l t f t i l d th i tidevelopment of new materials and the innovative cooling techniques.

2. Increasing the efficiencies of turbo-machinery components.

3. Adding modifications to the basic cycle such as incorporating intercooling, regeneration, and

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reheating techniques.A more recent gas turbine manufactured by GE use 1425oC turbine inlet temperature, 282 MW, and 39.5% efficiency in the simple-cycle mode.

Deviation of Actual Gas-Turbine Cycles from Idealized OnesThe deviation of actual compressor and turbine behavior from the idealized isentropic behavior can be accurately accounted for by utilizing the isentropic efficiencies of the turbine and compressor defined as (equations at bottom right). Where states 2a and 4a are hh

44

Where states 2a and 4a are the actual exit states of the compressor and the turbine, respectively, and 2s and 4sare the corresponding states for isentropic case. s

a

s

aout,turb

a

s

a

scomp,isen

hhhh

ww

hhhh

ww

43

43

12

12

−−

≅=

−−

≅=

η

η

and,

23

The Brayton Cycle with Regeneration

In gas-turbine engines, the temperature of the exhaust gas leaving the turbine is often considerably higher than the temperature of the air leaving the compressor. Therefore the high pressure air leaving the compressor

45

Therefore, the high-pressure air leaving the compressor can be heated by transferring heat to it from the hot exhaust gases in a counter-flow heat exchanger, which is also known as a regenerator or a recuperator (as shown in the figure above.)

T-s Diagram of a Brayton Cycle with RegenerationThe thermal efficiency of the Brayton cycle increases as a result of regeneration since the portion of energy of the exhaust gases that is normally rejected to the surroundings is now used to preheat the air entering the combustion chamber.

rregenerato ideal an approaches rregenerato a whichto extent The

46

. utilized, are sassumption standard-air-cold the When

as defined is and esseffectiven the called is

24

25

24

25

TTTT

.hhhh

qq

εmaxregen,

act,regen

−−

≅

−−

==

ε

ε

24

Thermal Efficiency of the Ideal Brayton Cycle with and without RegenerationThe use of a regenerator with a very high effectiveness (0.85 in practice) cannot be justified economically unless the savings from the fuel costs exceed the additional expense involved.

Under the cold-air-standard assumptions, the thermal ffi i f id l B t

47

( )( ) r 1-kp

k/regen,th T

T

−=

3

11η

efficiency of an ideal Brayton cycle with regeneration is shown at right, which operates most effectively at lower rp and (T1/T3) ratios.

Many of the impracticalities associated with the Carnot cycle can be eliminated by

Rankine Cycle: The Ideal Cycle for Vapor Power Cycles

y ysuperheating the steam in the boiler and condensing it completely in the condenser, as shown schematically on a T-sdiagram in the figure (on next slide) The cycle that

48

next slide). The cycle that results is the Rankine cycle, which is the ideal cycle for vapor power plants.

25

Rankine Cycle (continued)

1→2 Isentropic compression

The Ideal Rankine cycle does not involve any internal irreversibilities and consists of the following four processes:1→2 Isentropic compression

in a pump

2→3 Constant pressure heat addition in a boiler (steam generator)

3→4 Isentropic expansion in a

49

turbine

4→1 Constant pressure heat rejection in a condenser (water or dry air cooling)

Energy Analysis of the Ideal Rankine CycleAll four processes that make up the Rankine cycle can be analyzed as steady-flow processes. The steady-flow energy equation per unit mass of steam reduces to

( ) ( ) ieoutinoutin hhwwqq −=−+−( ) ( ) ieoutinoutin qq

The boiler and the condenser do not involve any work, and the pump and the turbine are assumed to be isentropic, thus,

( )

1111

12120

hh

PPhhwq

P@fP@f

in,pump

=≅=

−=−==

and where

:)( Pump

υυυ

υ

50

14

43

23

1111

00

0

hhqwhhwq

hhqw

out

out,turb

in

P@fP@f

−==

−==−==

:)( Condenser :)( Turbine

:)( Boiler

26

Thermal Efficiency of the Ideal Rankine CycleThermal efficiency of the ideal Rankine cycle is determined from

outoutinin,pumpout,turbnetth q

qq

qqq

wwqw

−=−

=−

== 1ηinininin qqqq

The conversion efficiency of power plants in the United States is often expressed in terms of heat rate, which is the amount of heat supplied, in Btu, to generate 1 kWh of electricity.

( )( )

kWh/Btuth

3412=η

51

( )Btu/kWhth rateHeatη

For example, a heat rate of 11,363 Btu/kWh is equivalent to 30 percent thermal efficiency, the smaller the heat rate, the greater the efficiency.

Deviation of Actual Vapor Power Cycle from Idealized Ones

12

12hhhh

ww

a

s

pump,a

pump,spump,isen −

−==η

s

a

turb,s

turb,aturb,isen hh

hhww

43

43−−

==η

52

27

Things to be Considered in Evaluating the Performance of Actual Power Cycle

The irreversibilities occurring within the pump and the turbine.

Fl id f i ti d i th b il thFluid friction causes pressure drops in the boiler, the condenser, and the piping between various components.

Heat loss from the steam to the surroundings.

Heat losses occur at the bearings between the moving parts as a result of friction.

St th t l k t d i th l d i th t l k

53

Steam that leaks out during the cycle and air that leaks into the condenser.

Power consumed by the auxiliary equipment such as fans that supply air to the furnace.

The basic idea behind all the modifications to increase the thermal efficiency of the power cycle is the same:

How Can We Increase the Efficiency of the Rankine Cycle?

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.

That is, the average fluid temperature should be as high as possible during heat addition and as low as

54

g p gpossible during heat rejection. There are three ways of accomplishing this for the simple ideal Rankine cycle.

28

1. Lowering the Condenser PressureThe colored area on the T-sdiagram represent the increase in net work output as a result of lowering the condenser pressuref P t P ’ Th h tfrom P4 to P4’. The heat requirement also increase (represented by the area under curve 2’-2), but this increase is very small. Thus the overall effect of lowering the condenser pressure is an increase in the

55

pthermal efficiency of the cycle.For effective heat transfer (∆T = 10oC), the pressure must be above ? kPa for a condenser to be cooled by a nearby river at 15oC. (The drawbacks are air leak and moisture content.)

2. Superheating the Steam to High TemperaturesThe colored area on this diagram represents the increase in the net work. The total area under the process curve 3-3’ represents the increase in therepresents the increase in the heat input. The overall effect is an increase in thermal efficiency. Superheating the steam to higher temperatures has another very desirable effect: It decreases the moisture content of the steam at

56

the turbine exit.

The temperature to which steam can be superheated is limited, however, by metallurgical considerations. Presently the highest steam temperature allowed is about 620oC. Ceramics!

29

3. Increasing the Boiler PressureAnother way of increasing the average temperature during the heat-addition process is to increase the operating pressureof the boiler which automaticallyof the boiler, which automatically increase the temperature at which boiling takes place. The effect of increasing the boiler pressure on the performance of vapor power cycle is illustrated on a T-s diagram in the figure at

57

right.

The undesirable side effect as shown in the diagram above can be corrected by reheating the steam. Usually nuclear plant (ηth= 34%) is lower than fossil-fuel plant (40%) for safety reason.

How can we take advantage of the increased efficiencies at high boiler pressures without facing the problem of excessive moisture at the final stages of the turbine?

The Ideal Reheat Rankine Cycle

1 S h t th t1. Superheat the steam to a very high temperature Not to over the metallurgical unsafe levels.

2. Expand the steam in the turbine in two

58

the turbine in two stages, and reheat it in between.

30

The T-s diagram of the ideal reheat Rankine cycle is shown in the figure below. The total heat input and the total turbine work output for a reheat cycle become

The T-s Diagram of Ideal Reheat Rankine Cycle

( ) ( )4523 hhhhqqq reheatprimaryin −+−=+= ( ) ( )( ) ( )654321

4523

and hhhhwww

qqq

,turb,turbout,net

reheatprimaryin

−+−=+=

1. The incorporation of the single reheat in a modern power plant improve the cycle efficiency by 4 to 5%.

2. The use of more than two reheat

59

stages is not practical.

3. If we had materials that could withstand sufficiently high temperatures, there would be no need for the reheat cycle.

Example IV-4.2:The Ideal Reheat Rankine CycleConsider a team power plant operating on the ideal reheat Rankine cycle. Steam enters the high-pressure turbine at 15 MPa and 600oC 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 turbine is not to exceed 10.4 percent, determine(a) the pressure at which the steam should be reheated and (b) the thermal efficiency of the cycle. Assuming the steam is reheated to

60

Assuming the steam is reheated to the inlet temperature of the high-pressure turbine. <Answers: (a) 4.0 MPa, (b) 45.0%>

Solution:

31

( ) the that trequiremen the from determined is pressure reheat The :Analysis

.negligible are changesenergy potential andKinetic 2.exist. conditions operatingSteady 1.

:sAssumption

a

Thus,

; :6 State

same.thebe6and 5 states atentropies

K.kg/kJ....hxhh

K.kg/kJ....sxss.xkPaP

fgf

fgf

8233582392896083191

370750097896064930896010

66

66

66

=×+=+=⇒

=×+=+=⇒==

6110.4%. above content moisture a prevent tolower or MPa 4 of pressure a at reheated be should steam Therefore,

:5 State

Thus,

MPa.P

kg/kJ.hCoT

ss045

436745

600565

==⇒

=

=

( )

( ) ( ) 141510150000010100

; 15 :2 State00101008319100 ; 10 :1 State

:statesother allat enthalpies theknow toneed we,efficiency thermal thedetermine To

3121

122

31111

kg/kJ.kPakg/m.PPvw

ssMPaPkg/m.v,kg/kJ.h.xkPaP

b

i =−×=−=

==

==⇒==

( ) ( )

( ) ( ) ( ) ( )433895

33154436749720633582 Thus, 5375 ,33154 ,4 :4 State

67766 ,33582600 ,15 :3 State

97206141583191

141510150000010100

4523

44344

3333

12

121

kg/kJ.....hhhhq C.Tkg/kJ.hssMPaP

K.kg/kJ.skg/kJ.hCTMPaP

kg/kJ...whh

kg/kJ.kPakg/m.PPvw

in

o

oin,pump

in,pump

=

−+−=−+−=

==⇒==

==⇒==

=+=+=

×

62

( )45.0%or 450043389597214311 and

972143831918233516

...

qq

kg/kJ...hhqg

in

outth

out

=−=−=η

=−=−=

32

Ideal Regenerative Rankine Cycle with Open Feedwater HeaterAnother way of increasing the thermal efficiency of the Rankine cycle is by regeneration. During a regeneration process, liquid water (feedwater) leaving the pump is heated by some steam bled off the turbine at some intermediate pressure in devices called feedwater heaters.

63

Ideal Regenerative Rankine Cycle with Closed Feedwater HeaterThe two streams are mixed in open feedwater heaters, and the mixture leaves as a saturated liquid at the heater pressure. In closed feedwater heaters, heat is transferred from the steam to the feedwater without mixing.

64

33

A Steam Power Plant with One Open and Three Closed Feedwater Heaters

65

An Ideal Cogeneration PlantThe production of more than one useful form of energy (such as process heat and electric power) from the same energy source is called cogeneration Cogenerationcalled cogeneration. Cogeneration plants produce electric power while meeting the process heat requirements of certain industrial processes. This way, more of the energy transferred to the fluid in the boiler is utilized for a useful

Th f ti f

66

purpose. The fraction of energy that is used for either process heat or power generation is called the utilization factor of the cogeneration plant.

34

More Ways to Increase Power plant Thermal EfficiencyThe overall thermal efficiency of a power plant can be increased by using binary cycles or combined cycles A binary cycle is composed of two separatecycles. A binary cycle is composed of two separate cycles, one at high temperatures (topping cycle) and the other at relatively low temperatures. The most common combined cycle is the gas-steam combined cycle where a gas-turbine cycle operates at the high-temperature range and a steam-turbine cycle at the low-temperature range. Steam is

67

y p gheated by the high-temperature exhaust gases leaving the gas turbine. Combined cycles have a higher thermal efficiency than the steam- or gas-turbine cycles operating alone.

Mercury-Water Binary Vapor Cycle

68

35

Combined Gas-Steam Power Plant

69

Steam TurbinesThe turbine is a device that converts the stored

mechanical energy in a fluid into rotational mechanical energy. There are several different types, including steam, gas, water, and wind turbines.

There are several ways to classify steam turbines:1. With respect to the purpose of the turbine:

• Central-station units which are used to drive electrical generators at synchronous speed.

• Superposed or topping steam turbines are high-

70

• Superposed or topping steam turbines are high-pressure turbines that are installed in older, low-pressure steam systems to improve the overall efficiency of the power plant.

• Mechanical-drive turbines to power large draft fans.

36

2. According to the exhaust or back pressure of the unit:• Either condensing or noncondensing. In the

noncondensing turbine, the turbine-exhaust pressure is above or equal to atmospheric pressure and the system can operate with or without a condenser, If there is no condenser, this system will require continuous water

3. According to the method of steam injection or extraction from the turbine:• Bleeder or extraction turbines are used where turbine

steam is removed partway through the turbine for process use or for feedwater heating.

71

p g• Reheat turbines are used in the reheat vapor-power

cycles.• Extraction-induction turbines have ports for both the

extraction and injection of steam at intermediate points in the turbine.

Turbine Blading

There are twobasic types of turbine baldingbalding, impulse and reaction. Two different types of impulse staging and a typical

ti t

72

reaction stage are shown in the figure at right:

37

The velocity vectors in the tangential and axial directions of the turbine rotor are shown in the figure below. The force on the moving blade, Fb is equal to mat, or letting m_dot represent the steam flow rate through the blade,

Energy Transferred to the Moving Blades

Then, the energy transferred to the moving blades Pb is:( ) ( )

( ) ( )[ ]22

21

22

21

2121

2 r,r,

bbt,t,bbb

VVVVmVcosVcosVmVVVmVFP

−−−=

+=−==

&

&& δα

73

The performance of a given blade is given by the blade efficiency, which is defined as the fraction of the kinetic power of the inlet steam that is transferred to the blade, or

Blade Efficiency

( ) ( ) ( )22222 VVVVVVV( ) ( ) ( )

2

1

2

21

22

21

22

21

21

21

1

2

−=

−−−=

−=

VV

VVVVV

VVVV r,r,bt,t,

Efficiency Blade

:to reduces equation above the flow, ssfrictionle For

Efficiency Blade

The blade efficiency and blade power are maximum when

74

The blade efficiency and blade power are maximum when V2 is a minimum and this occurs when V2,r is zero and V2is equal to V2,a. When there is no friction, V1,t = Vb,opt, i.e.,

αcosVVV t,

opt,b 2211 ===velocity Blade Optimum