Gaspowercycles

8/7/2019 Gaspowercycles

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Reciprocating engines

(internal combustion)

Reciprocating engines

(internal combustion)


2/35


3/35

Ericsson cycleEricsson cycle

same as Stirling cyclesame as Stirling cyclewit h th e P=const processeswit h th e P=const processessubstituted for v=constsubstituted for v=constsh ould involve regenerationsh ould involve regenerationimpracticalimpractical

s

P=const

Ex ample 9.9Ex ample 9.9

regenerationregeneration


4/35

Efficiency of Stirling andEricsson cycles wit h

regeneration

Efficiency of Stirling andEricsson cycles wit h

regeneration

11 s ts t law for thi s cycle:law for thi s cycle: W Q QH L!

energy conver s ion efficiency i s :energy conver s ion efficiency i s :

L ! ! !useful work heat input

W Q

Q QQ

H

H L

H

H

L

H

L

T

T

Q

Q!! 11L

E fficiency i s the s ame a s for E fficiency i s the s ame a s for Carnot Cycle but it would beCarnot Cycle but it would be

much lower if regenerationmuch lower if regenerationwere not pre s entwere not pre s ent


5/35


6/35

Cylinder Cylinder


7/35

V alveV alve


8/35


9/35

4- stroke engine4- stroke engine


10/35


11/35

4- stroke engine4- stroke engine


12/35

A ctual Otto cycleA ctual Otto cycle

PP

VV


13/35

A ir - Standard

Power Cycles

A ir - Standard

Power CyclesA ssumptions:A ssumptions:

we analyse a control mass of we analyse a control mass of an ideal gas, meaning.....an ideal gas, meaning.....exh aust and air intake areexh aust and air intake aresubstituted wit h h eat transfer substituted wit h h eat transfer

from t h e system to t h efrom t h e system to t h esurroundingssurroundingscombustion is replaced bycombustion is replaced byh eat transfer from an externalh eat transfer from an externalsource to t h e systemsource to t h e systemall processes are internallyall processes are internallyreversible, meaning....reversible, meaning....

gas specific h eat is constantgas specific h eat is constant


14/35

I deal Otto

Cycle

I deal Otto

CycleA pproximates a spark A pproximates a spark -- ignition engineignition engine

ss

v v

QH

QL

s=const

QH

QL

v=const


15/35

I deal Otto

Cycle (cont.)

I deal Otto

Cycle (cont.)11 s ts t law for thi s cycle:law for thi s cycle: W Q QH L!



W Q

Q QQH

H L

H

L ! ! 1 1 4 13 2

QQ

mC

mC L

H

v

v

L ! 11

1

1 4 1

2 3 2

T T T

T T T


16/35

I deal Otto

Cycle (cont.)

I deal Otto

Cycle (cont.)P v const k !for an i s entropic proce ss :for an i s entropic proce ss :

P v P vk k 1 1 2 2!

T

T

V

V

V

V

T

T

k k

2

1

1

2

1

4

3

1

3

4!

!

!

in ca s e of an ideal ga s :in ca s e of an ideal ga s :

T

T

T

T

3

2

4

1

!

L ! ! ! 1 1 11

2

1

2

1

1T

T

V

V r

k

v

k

compre ss ioncompre ss ionratioratio


17/35

I deal Otto Cycle

(cont.)

I deal Otto Cycle

(cont.)


18/35


19/35

Otto Cycle (cont.)Otto Cycle (cont.)

Deviations of the Otto cycleDeviations of the Otto cyclefrom an openfrom an open- -cycle spark cycle spark- -ignition engineignition engineCp, Cv increase wit h Cp, Cv increase wit h temperaturetemperature

combustion (incomplete)combustion (incomplete)replaces t h e h eat transfer processreplaces t h e h eat transfer processpressure drop across t h e ex h austpressure drop across t h e ex h austvalvesvalvesh eat transfer between t h e gas andh eat transfer between t h e gas andth e cylinder wallsth e cylinder wallsirreversibility associated wit h irreversibility associated wit h

pressure and temperaturepressure and temperaturegradientsgradients


20/35

s

'

'

'

''

v

Closed Brayton

cycle (cont.)

Closed Brayton

cycle (cont.)QH

QL

s=const

QH

QL

p=const


21/35

Efficiency of a

Brayton cycle

Efficiency of a

Brayton cycle11 s ts t law for thi s cycle:law for thi s cycle: W Q QH L!



W Q

Q QQH

H L

H

L ! ! 1 1 4 13 2

QQ

mC T T

mC T T L

H

P

P

L ! 11

1

1 4 1

2 3 2

T T T

T T T

ff fff f


22/35

Efficiency of a

Brayton cycle (cont.)

Efficiency of a

Brayton cycle (cont.)for an i s entropic proce ss :for an i s entropic proce ss :

P P V V k

1 2 2 1!

T

T

P

P

P

P

T

T

k k

k k

2

1

12

1

3

4

3

4

1

! ! !

in ca s e of an ideal ga s :in ca s e of an ideal ga s :

T T

T T

3

2

4

1

!

L ! ! 1 112

1

2

1

T T

P P

k k

PV P V T T 1 1 2 2 1 2!

P v const k !

Effi i fEffi i f


23/35

Efficiency of a


Efficiency of a


is entropicis entropic

press

urepress

ureratioratio

L ! 1

1

2 1

1

P P k

k

0

10

20

30

40

50

60

0 5 10 15

P re ssu re ra ti o

Thermal efficiency %


Th lTh l


24/35

Th e actual gas

turbine process

Th e actual gas

turbine process

s

T

1

42 4s2 s

L compsh h

h h

! 2 12 1

L turbs

h hh h

! 3 43 4


B t lB t l


25/35

Brayton cycle

with

regeneration

Brayton cycle

with

regeneration

v

P

1 4

2 3

y

s

T

14

2 '

3

2 y

3 '

x

a c d

Effi i fEffi i f


26/35

Efficiency of a

regenerative cycle

Efficiency of a

regenerative cycleL ! ! !net wor

heat in tw

qw w

qH

t c

H

q h h C T T H x P x! ! 3 3

w h h C T T

t P ! ! 3 4 3 4

for an ideal regenerator:for an ideal regenerator:

T T x4

w qt H !

s o:s o:

Effi i fEffi i f


27/35

Efficiency of a

regenerative cycle

Efficiency of a

regenerative cycle

L ! ! 1 1 2 1

3 4

w

w

C T T

C T T

c

t

P

P

1

11

434

121!

T T T

T T T L

for an i s entropic proce ss :for an i s entropic proce ss :

T

T

P

P

P

P

T

T

k

k

k

k 2

1

12

1

3

4

3

4

1

! ! !

4

1

1 T T

!

Closed BraytonClosed Brayton


28/35

heatheate x changer e x changer

Closed Brayton

cycle

Closed Brayton

cycle

22

11 44

turbineturbinecompre ss or compre ss or

W W net net

QQH H

QQLL

heatheate x changer e x changer

33


29/35

Open Brayton cycleOpen Brayton cycle

turbineturbine

e x hau s te x hau s t

compre ss or compre ss or

air intakeair intake

combu s tioncombu s tionchamber chamber

Gas turbine cycleGas turbine cycle

fuelfuel

W W net net

Brayton cycleBrayton cycle


30/35

Brayton cycle

with

regeneration

Brayton cycle

with

regeneration

turbineturbine


compre ss or compre ss or

air air intakeintake


fuelfuel

W W net net

regenerator regenerator

xx

11

22

33

yy

M odified BraytonM odified Brayton


31/35

M odified Brayton

cycle

M odified Brayton

cyclemultimulti --stage compression wit h stage compression wit h intercoolingintercoolingmultimulti --stage expansion wit h stage expansion wit h reh eatreh eat

s

T

3

8

47

1

6

5

2 9

10

M odified BraytonM odified Brayton


32/35

M odified Brayton

cycle

M odified Brayton

cycle

turbine sturbine s


compre ss or scompre ss or s


regenerator regenerator 99

8811

55

66 77

1010

fuelfuel

air air

intakeintake

22 33

intercooler intercooler

44

Brayton cycle forBrayton cycle for


33/35

Brayton cycle for

jet propulsion

Brayton cycle for

jet propulsion

turbineturbine e x hau s te x hau s tcompress or compre ss or

air air intakeintake

combus

tioncombus

tionchamber chamber fuelfuel

22

33

5544

11

Ex ample 9. 10Ex ample 9. 10

Th e DieselTh e Diesel


34/35

Th e Diesel

Cycle

Th e Diesel

Cycle

v

P

14

2

3'

4'

3 3''

s

T

1

42'

3

2 4'

3' 3''

Ideal cycle for the Die s el engineIdeal cycle for the Die s el engine

QH

QL

s=const

v=const

P=const

Th e DieselTh e Diesel


35/35

e Diesel

Cycle(cont.)

e Diesel

Cycle(cont.)

11 s ts t law for thi s cycle:law for thi s cycle: W Q QH L!



W Q

Q QQH

H L

H

L ! ! 1 1 4 13 2

QQ

mC T T

mC T T L

H

v

P

L ! 11

1

1 4 1

2 3 2

T T T

k T T T

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