Production of Power From Heat [Compatibility Mode]

8/2/2019 Production of Power From Heat [Compatibility Mode]

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Production of Power fromHeat

MLP Dalida


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Carnot Engine

1-2 Reversible isothermal process: QH is absorbedfrom hot reservoir at temp TH

2-3 Reversible adiabatic process: TH decreased to TC3-4 Reversible isothermal process: QC is rejected to

cold reservoir at temp TC

4-1 Reversible adiabatic process : TC increase to TH


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Carnot Cycle

Difficulties:

High liquid content in exhaust of turbine chwhich causes corrosion

Difficult to find a pump that takes in mixtureof liquid and vapor and discharges it assaturated liquid


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Rankine Cycle

1 - 2: A constant pressure heating process in a boiler.

2 - 3: Reversible, adiabatic (isentropic) expansion of vapor in aturbine to the pressure of the condenser.

3 - 4: A constant-pressure, constant-temperature process in acondenser to produce saturated liquid at point 4.

4 - 1: Reversible, adiabatic (isentropic) pumping of saturatedliquid to the pressure of the boiler, producing compressed

(subcooled) liquid.


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S

fs

cv WQmzguH

dt

mUd&&& +=

+++

2

2

1)()( 12 HHmHmWS == &&

&

12 HHHWS ==

The maximum shaft work: a reversible process (i.e., isentropic, S1 = S2)

SS HisentropicW )()( =

The turbine efficiency

SS

S

H

H

isentropicW

W

)()(

=

Values for properly designed turbines: 0.7~ 0.8


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Pressure increases: compressors, pumps, fans,

blowers, and vacuum pumps. Interested in the energy requirement

S

fs

cv WQmzguHdt

mUd&&& +=

+++

2

2

1)()( 12 HHmHmWS == &&

&

12 HHHWS ==

The minimum shaft work: a reversible process (i.e., isentropic, S1 = S2)

SS HisentropicW )()( =

The compressor efficiencyH

H

W

isentropicW S

S

S

=

)()(

Values for properly designed compressors: 0.7~ 0.8

Compression process


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Boiler and Condenser

Boiler- transfers heat from burning fuel to

the cycle

Condenser transfers heatnfrom cycle to

surroundings Energy equations:

HQHmQ == &

&


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Steam generated in a power plant at a pressure of 8600 kPa and a temperature of

500C is fed to a turbine. Exhaust from the turbine enters a condenser at 10 kPa,

where it is condensed to saturated liquid, which is then pumped to the boiler. (1)What is the thermal efficiency of a Rankine cycle operating at these conditions?

(2) What is the thermal efficiency of a practical cycle operating at these conditions

if the turbine efficiency and pump efficiency are both 0.75? (3) If the rating of the

power cycle of part (2) is 80000kW, what is the steam rate and what are the heat-

transfer rates in the boiler and condenser?

The turbine (2 3) : ( )

kg

kJHisentropicW

Ss 2.1274)( ==kg

kJH 4.21773 =

The enthalpy of saturated liquid at 10 kPa:kg

kJH 8.1914 =

The condenser (3 4):kg

kJHHQ 6.192534 ==

The pump (4 1): ( )kg

kJHisentropicW Ss 7.8)( ==

kg

kJH 5.2001 =

(1) The enthalpy of superheated steam at 8600 kPa and 500 C:kg

kJH 6.33912 =

The boiler (1 2):kg

kJHHQ 1.319112 ==

3966.01.3191

7.82.1274||

|)(| =+

=boiler

s

QRankineW)()()( condenserQboilerQRankineWs =


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(2) With a turbine efficiency of 0.75: ( )kg

kJHturbineW Ss 6.955)( ==

kg

kJHHH 0.243623 =+=

The condenser (3 4): kg

kJ

HHQ 2.224434 ==

The pump (4 1): ( )kg

kJHpumpWs 6.11)( ==

The net work of the cycle is: kg

kJ

netWs 0.9446.116.955)( =+=&

kg

kJHHH 4.20341 =+=

The boiler (1 2): kg

kJHHQ 2.3188

12

==

2961.02.3188

0.944

||

|)(|==

boiler

s

Q

netW

The enthalpy of saturated liquid at 10 kPa: kgkJ

H 8.1914 =

power rating of 80000kW

)()( netWmnetW ss && =(3)

skgm 75.84

0.94480000 =

=&

s

kJboilerQmboilerQ 270200)()( == &&

skJcondenserQmcondenserQ 190200)()( == &&


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REGENERATIVE CYCLE


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Internal-combustion engines

Steam power plant:

steam is an inert medium to which heat is

transferred from a burning fuel or from a nuclearreactor

Steam absorbs heat at a high temperature in the boiler.

Steam rejects heat at a relatively low temperature in the

condenser.

Internal combustion engine:

No working medium

a fuel is burned within the engine and the combustionproducts serve as the working medium.

High temperatures are internal and do not involve heat-transfer surfaces.

Air as the working fluid


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Otto Engine


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Otto Engine

)(0rejectionheatolumeconstant v:C-BStep

)(,0

expansionadiabaticreversible:B-Atep

)(0

additionheatolumeconstant v:A-DStep

)(,0

ncompressioadiabaticreversible:D-Ctep

BCVBCBCBC

ABVABABAB

DAVDADADA

CDVCDCDCD

TTCUQW

TTCUWQ

S

TTCUQW

TTCUWQ

S

===

===

===

===


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Otto Engine

1

11

rationcompressior:

1

=

==

r

VVr

Define

TT

TT

Q

W

O

D

C

DA

CB

DA

net

O


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The Otto EngineThe most common internal-combustion engine, because of it used in automobiles.

1st stroke: 0 1: At essentially constant pressure, a piston moving outward

draws a fuel/air mixture into a cylinder.2nd stroke: 1 2 3: all valves are closed, the fuel/air mixture is compressed,

approximately adiabatically along 1 2; the mixture is then ignited, and

combustion occurs so rapidly that the volume remains nearly constant while the

pressure rises along 2 3.

3rd stroke: 3 4 1: the work is produced. Approximately adiabatically

expand 3 4; the exhaust valves opens and the pressure falls rapidly at nearly

constant volume along 4 1.4th stroke: 1 0: the piston pushes the remaining combustion gases from the

cylinder.

The compression ratio:D

C

V

V

volumeendthe

volumebeginningther =

The efficiency of engine (i.e., the work produced per unit quantity of fuel)

The air-standard Otto cycle: two adiabatic and two constant-volume steps, which

comprise a heat-engine cycle for which air is the working fluid.


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DA

CB

DAV

BCVDAV

DA

BCDA

DA

TTTT

TTC

TTCTTC

Q

QQ

Q

netW

=

+=

+=

1

)(

)()(

||

|)(|

Fig 8.9, the thermal efficiency

Ideal gas

=

=

DA

CB

DA

CB

D

C

PP

PPr

PP

PP

V

V11

AD VV = CBDA VPVP =

BC VV =

DDCCVPVP =

D

C

DA

CB

P

P

rPP

PP

r =

= 11/

1/

1

=

=

rV

V

P

P

C

D

D

C 1

11

11

1

=

=

rr

r


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The diesel engine Differs from the Otto engine: the temperature at

the end of compression is sufficiently high thatcombustion is initiated spontaneously. Higher compression ratio the compression step to

a higher pressure higher temperature results.

The fuel is injected at the end of the compressionstep

The fuel is added slowly enough the combustionprocess occurs at approximately constant pressure.

At the same compression ratio:

However, the diesel engine operates at highercompression ratios and consequently at higher

efficiencies.

dieselOtto >


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Diesel Engine


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Diesel Engine

)(0

rejectionheatolumeconstant v:C-BStep

)(,0

expansionadiabaticreversible:B-Atep

)-()(

)()-(

additionheatpressureconstant:A-DStep

)(,0

ncompressioadiabaticreversible:D-Ctep

BCVBCBCBC

ABVABABAB

DADDAVDADADA

DAVDADADADDA

CDVCDCDCD

TTCUQW

TTCUWQ

S

VVPTTCWUQ

TTCUQVVPW

TTCUWQ

S

===

===

==

===

===


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Diesel engine

)1(111

V

Vratio:

))((

)(-1

1

D

A

=

+

=

++==

C

CD

C

DAV

CBV

DA

ABDACD

DA

netD

rr

r

offcutrDefine

TTRC

TTCQ

WWW

Q

W


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ExampleAn air-standard Diesel cycle absorbs

1,500J/mol of heat (step DA whichsimulates combustion). The pressure andtemperature at the beginning of the

compression step are 1 bar and 20oC andthe pressure at the end of compressionstep is 4 bar. Assuming air to be an ideal

gas for which Cp=(7/2)R and Cv=(5/2)R,what are the compression ratio and theexpansion ration of the cycle?


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1

(1 )/

1

1.357

1500 / ( ) 515.845

2.841

C C D D

C D

D C

D D

C C

DA

DA P D A A

C

C C CB A

eAA A A C

A

A D

e

P V P V

V Pr

V P

r

TP const

T P

T P

Q J molQ C T T T K

RT

V P TV P

r RTV V T P

P

P P

r

=

= =

=

=

=

== =

= = = =

=

=


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the heat quantities absorbed in step DA: )( DAPDA TTCQ =

the heat rejected in step BC:)(

BCVBC

TTCQ =

the thermal efficiency:

=

=

=

+=+=

rr

rr

rr

rrrr

TTTT

TTCTTC

QQ

e

e

e

ee

DA

BC

DAP

BCV

DA

BC

/1/1

)/1()/1(11

/1

)/1)(/()/1(11

11)()(11

11

Reversible, adiabatic expansion (step AB):11

=

BBAA VTVT

Reversible, adiabatic compression (step CD):11

=

CCDD VTVT

On the basis of 1 mol of air (ideal gas),

The compression ratio: DC CVr / The expansion ratio: ABeCVr /


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The gas-turbine engine The Otto and diesel engines use the high energy of high-

temperature, high-pressure gases acting on the piston

within a cylinder. However, turbines are more efficientthan reciprocating engines.

The advantages of internal combustion are combinedwith those of the turbine.

The air is compressed to several bars and enters thecombustion chamber.

The higher the temperature of the combustion gases

entering the turbine, the higher the efficiency of the unit. The centrifugal compressor operates on the same shaftas the turbine, and part of the work of the turbine servesto drive the compressor.


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The compressor compresses the incoming air. Because of this extreme

compression, the air is heated up in the process. Heated and very highpressure air makes its way into the combustion chamber. The combustion

chamber has a glow plug similar to the glow plug in a basic glow engine.

When the air in the combustion chamber reaches the appropriate temperature

and pressure, a fine mist of fuel is introduced and the glow plug is lit. The fuelexplodes pushing the exhaust gases through the turbine


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Gas Turbine EngineWorking fluid: air w/c is considered as ideal

gas with constant heat capacity

The Brayton cycle:

AB reversible adiabatic compression.

BC heat QBC is added.

CD isentropic expansion.

DA constant-pressure cooling.


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B d 1 l f i th th l ffi i ABCDWWnetW |||)(|


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Based on 1 mol of air, the thermal efficiency:BC

ABCD

BC QQ=

||

)(

The work done as the air passes through the compressor:

)(ABPABAB

TTCHHW ==

The heat addition:

)( BCPBC TTCQ =

Isentropic expansion in the turbine:

)(|| DCPCD TTCW =

BC

AD

TT

TT

= 1

Isentropic expansion:

)1(

=

A

B

A

B

P

P

T

T

)1()1(

=

=

B

A

C

D

C

D

P

P

P

P

T

T

)1(

1

=

B

A

P

P


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JET ENGINE

JET ENGINE


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1. A fan at the front sucks the cold air into the engine.2. A second fan called a compressor squeezes the air (increases its pressure)by about eight times. This slows the air down by about 60 percent and it's speedis now about 400 km/h (240 mph).3.Kerosene (liquid fuel) is squirted into the engine from a fuel tank in theplane's wing.

4.In the combustion chamber, just behind the compressor, the kerosene mixeswith the compressed air and burns fiercely, giving off hot exhaust gases. Theburning mixture reaches a temperature of around 900C (1650F).5.The exhaust gases rush past a set of turbine blades, spinning them like awindmill.6. The turbine blades are connected to a long axle (represented by the green

line) that runs the length of the engine. The compressor and the fan are alsoconnected to this axle. So, as the turbine blades spin, they also turn thecompressor and the fan.7.The hot exhaust gases exit the engine through a tapering exhaust nozzle.The tapering design helps to accelerate the gases to a speed of over 2100 km/h

(1300 mph). So the hot air leaving the engine at the back is traveling over twicethe speed of the cold air entering it at the frontand that's what powers theplane.

JET ENGINE


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JET ENGINE


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JET ENGINE


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ROCKET ENGINE

ROCKET ENGINE


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ROCKET ENGINE

Date post:	05-Apr-2018
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Production of Power From Heat [Compatibility Mode]

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