heat engines2

8/3/2019 Heat Engines2

1/21

Heat EnginesEnergy Resources:

Fossil fuels, biomass, nuclear, solar, wind, ocean ( waves, ocean temp.

energy conversion OTEC)

Thermodynamic relations:

First Law:

SystemSSSFdHdWdQ

SystemCloseddUdWdQ

.........................

.......................

=

=

Perfect Gas:

)./...(8314

..........................1

................1

....................................

...............................

KkgjG

RTuhM

GR

k

kRC

k

RC

pvuhC

Ck

dTdhC

dTduC

RTpvmRTPV

pv

c

ppv

=

+==

=

=

+====

==

p p

2

1 = pdVW = VdpW

2 1

V V

Second Law: 2

1

Power Plant Generator

Steam power

plants

Hydraulic

power plants

Gas power plants

Gas turbinesReciprocating engines

Petrol Diesel Stirling


2/21

TdSdQ = Q

1

2

1

2

12 ln.lnV

VR

T

TCSS v += .(1) 1

1

2

1

212 ln.ln

ppR

TTCSS p = ...(2)

p V=Const

pVn=Const

P=Const (n=0)

T=Const (n=1)

PVk=Const (n=k)

T

PVk=C

V=C

P=C

T=C

S

2


3/21

Const.

Volume

(Isochoric)

Const.

Pressure.

(Isobaric)

Const.

Temp.

(Isothermal)

Adiabatic

Reversible

(Isentropic)

Polytropic

Relations V=const

1

2

1

2

T

T

p

p=

2

1

2

1

.

T

T

V

V

Constp

=

=

constU

VpVp

ConstT

=

=

=

2211 .

.

k

k

k

k

p

p

V

V

T

T

ConstpV

ConstS

1

1

2

1

2

1

1

2

.....

=

=

=

= ConstVp n =.

Work W= 0 Vp.

1

2ln.V

VmR

0

..

=

=

Q

UW

TCm v

n

TTRm

1

.(. 12

Heat Q= TCm v .. TCm p ..

WQ

U

V

VTRm

=

= 0

ln...1

2 0 WUQ +=

Entropy=S

1

2ln..

T

TCm v

1

2ln..

T

TCm p

1

2ln..

V

VRm

0 Relations

(1)&(2)

1

2

1

212 ln.ln

V

VR

T

TCSS v += ...(1)

1

2

1

2

12 ln.lnp

pR

T

TCSS p = ..(2)

Air Standard Cycles

Assumptions:

1-The working fluid is air (ideal gas PV=mRT) of fixed mass.

2-Combustion is replaced by a process of heat addition.

3-Cycle is completed by heat transfer to the surrounding.

4-All processes are reversible.

3


4/21

5-Constant specific heat.

Important Parameters:

1-Thermal efficiency:

add

netth

QW= p Wnet

2-Mean effective pressure:

s

mV

CycleW

VolumeStroke

CycledoneWork

p ==..

..

V

3-Work Ratio:

WorkGross

WorkNet

W

WWR

positive

net

...

...==

4-Specific Work Transfer:

plantofSizem

WSW

air

net ................=

5-Specific Consumption:

WSW

mCS

net

air

.

1. ==

Carnot Cycle:

4

Source TH

E

Sink TL

W=QH-QL

14

3

2p

32

1

T

V S

TH

TL

4QL

QH

Isothermal

Isentropic

1-2 Isentropic Compression

2-3 Isothermal Heat addition

3-4 Isentropic Expansion

4-1 Isothermal Heat rejection


5/21

From p-V diagram:

2

3

1

4

2

3

ln...

ln...ln...

V

VTRm

V

VTRm

V

VTRm

Q

QQ

Q

W

H

LH

H

LH

add

net

th

=

==

but1

4

2

3

V

V

V

V=

H

LLHth

TT

TTT

H

== 1

From T-S diagram:

)(.

).(.)(.

23

1423

SSTm

SSTmSSTm

Q

QQ

Q

W

H

LH

H

LH

add

netth

=

==

but 1423 SSSS =

H

LLH

th

T

T

T

TT

H

=

= 1

gross

net

W

WWR =

== ))(( 23 SSTTmQW LHnet

isentropicisothermalgross WWW += U=0 Q=0

W=Q W=U

))((

)()(

))((

)(.)(.

23

23

23

23

SSTTSW

TTCSST

SSTTWR

TTCmSSTmW

LH

LHvH

LH

LHvHgross

=

+

=

+=

Reciprocating engines cycles:Stirling Cycle:

5

1

S

2

3

41

43

2

V

Tp V=Const

Isothermal T=Const

1-2 Isothermal Compression2-3 Const. Volume Heat addition

3-4 Isothermal Expansion

4-1 Const. Volume Heat rejection


6/21

1

S

2

3

4 1

43

2

V

Tp V=Const

Isothermal T=Const

1-2 Isothermal Compression

2-3 Const. Volume Heat addition

3-4 Isothermal Expansion4-1 Const. Volume Heat rejection

4

3

1

2

1

2

12

3

434

...........ln..

ln..

V

V

V

Vbut

V

VTRmQ

V

VTRmQ

L

H

==

=

6


7/21

===

=

+=

==

LimitsTempsamethebetweenWorking

Carnot

H

L

H

LHth

H

HL

H

HL

add

th

TT

TTT

V

VTRm

V

VTRm

V

VTRm

V

VTRm

V

VTRm

V

VTRm

Q

WW

Q

dW

...................

1

2

1

2

1

2

3

4

3

4

1

2

34

3412

1

ln..

ln..ln..

ln..

ln..ln..

2

1234

34

1234

1ln)(

1

V

VTTRWWSW

T

T

W

WW

W

WWR

Lh

H

L

gross

net

=+=

=+

==

Both WR & SW are greater than the values for Carnot cycle.

+

=+

=

H

LHvH

L

LHvH

LH

T

TT

SS

CTT

TTCSSTSSTTWR

)(.

)(1

1)1()()(

))((

23

23

23

.Carnot

[ ] onethanloweris ................

CarnotStirling WRWR >

3-4ColdHot

Regenerator CoolerHeater

?

Expansion Compression

7

Stirling

Engine

0 90 180 270 360 Crank angle

Total

Volume

4-1 1-2 2-3 3-4

Compression Expansion

4-1 Transfer of working fluid to the cold space..Const vol.heat rejection to

the regenerator

2-3 Transfer of working fluid to the hot space..Const vol. Heat addition

from the regenerator


8/21

Otto Cycle:

8

p

V S

4

3

2

4

3

2

1

T

1

V1

V2

Isentropic Const. Volume

Wnet

Qadd

Qrej


9/21

Carnotk

v

th

k

v

kk

th

v

vv

th

vvnet

vrej

vadd

rT

T

V

V

T

T

RationCompressior

V

V

T

T

T

T

T

T

V

V

V

V

T

Tbut

T

T

T

T

T

T

TT

TT

TTCm

TTCmTTCm

TTCmTTCmW

TTCmvolconstQQ

TTCmvolconstQQ


10/21

Diesel Cycle:

10

1

V S

1

2

Tp

4

2 3

3

4

P=Const

V=Const

Isentropic

P=Const

T=Const


11/21

)1(

)1(1

1).(.

).(.1

).(.

).(.)(.

).(.)(.

).(.

).(.

2

3

2

1

4

1

23

14

23

1423

1423

1414

2332

=

=

=

=

==

==

T

TT

T

TT

kTTCm

TTCm

TTCm

TTCmTTCm

TTCmTTCmW

TTCmQQ

TTCmQQ

p

v

p

vp

th

vpnet

vrej

padd

..........)1(

1

.

11

1

1

.

11

...........

.................

2

3

1

2

3

2

3

1

2

3

1

2

3

2

31

1

2

1

4

3

2

3

1

4

1432

1

4

3

3

4

1

1

2

2

1

ratiooffcutV

Vwhere

kr

V

V

V

V

rk

VV

VV

VV

V

VV

V

TT

TT

VVVV

V

V

T

Tand

V

V

T

Tbut

k

k

k

kth

kk

k

k

kk

==

=

=

=

=

=

=

=

=

)..........(...................... smallisloadslowinhigherisloadondepends th

[ ]

ratiocomphighatoperateEnginesDieselBut

rratiocompsametheforOttoDiesel

Diesel

unitythangreaterOtto

kr

thth

k

kth

....................

..............)....()(

..

....................................

)1(

1

.

11

1


12/21

12

3

2

1

T

V

1

5

43p

S

5

4V=Const

Otto

Diesel

Isentropic

P=Const

ratiopressurep

pLet

TTkTT

TT

TTCmTTCm

TTCmTTCmTTCm

Q

W

TTCmVVpW

QQW

TTCmQQ

TTCmTTCmQQQ

th

pv

vpv

add

net

th

vpositive

rejaddnet

vrej

pvadd

.............

)()(

)(1

)(.)(.

)(.)(.)(.

)(.)(

)(.

)(.)(.

2

3

3423

15

3423

153423

5434

1551

34233423

=

+

=

+

+

==

+=

=

==

+=+=

12


13/21

k

k

k

k

k

k

k

kk

k

Tr

rTT

VVrVV

VV

VV

VV

V

V

V

V

V

VrT

V

VTT

rTV

VTT

rTp

pTTrT

V

VTT

......

......................

.

.

.

....

...

..,...........

1

1

1

15

32

13

24

13

34

1

4

5

4

1

5

41

1

1

5

4

45

1

1

3

4

34

1

1

2

3

23

1

1

1

2

1

12

=

=

=====

=

=

=

=

===

=

)(.)(

)(.)(.)(.

)(.)()(

tan................

............1................................................................

............1.........)1.(.()1(

1.11

5434

153423

153423

...

.

.1

TTCmVVp

TTCmTTCmTTCmWR

TTCTTCTTCSW

timporrsamethefor

rsamethefor

rsametheforif

kr

v

vpv

vpv

DieselthDualthOttoth

Dieselth

Ottoth

k

kth

+

+=

+=

>>

=

=

+

=

Gas Turbine Cycles: (Brayton or Joule)

13

1

2

3

2

1

T

V

1 4

3p

S

4

V=Const

P=Const

Isentropic

P=Const

44

C T

C.C

Qrej

Qadd

14

32

Wnet

Gas Turbine Cycle (Brayton cycle, or Joule cycle)


14/21

23

14

23

1423

1

)(.

)(.)(.

TT

TT

TTCmQ

TTCmTTCmW

th

padd

ppnet

=

=

=

powerOutputpowerTurbinepowerCompressor

powerTurbine

powerOutput

W

WWRNB

rT

T

TT

TTTTWr

r

p

p

T

T

T

TT

T

TT

T

T

p

p

p

p

T

Talso

r

rT

Tr

TT

ratioessurep

prand

rationCompressioV

VrLet

ve

net

k

k

p

k

k

p

th

k

k

th

k

k

k

k

k

v

th

k

v

k

v

p

v

.........

...

...........:

.1)(

)()(

.............1

1

11

)1(

)1(

1

.....

................1

1

........,

....Pr.......

............

1

2

1

43

1243

1

1

2

1

2

1

2

3

2

1

4

1

4

3

1

4

3

1

1

2

1

2

1

12

113

4

1

2

2

1

=

==

=

=

=

==

=

=

=

=

=

==

=

=

+

14


15/21

Report (M-1):

Hold a comparison among Otto, Diesel and Dual cycles in the following

conditions:

1-Same compression ratio and same heat input.2-Same maximum pressure and same heat input

3-Same maximum pressure and maximum temperature.

Draw the 3 cycles on the same P-V and T-S diagrams, compare the net

power and thermal efficiency.

15


16/21

16


17/21

17


18/21

18


19/21

19


20/21

20


21/21

heat engines2

Documents