[Flip-Side] 3. Thermodynamic Cycles

7/25/2019 [Flip-Side] 3. Thermodynamic Cycles

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Thermodynamic Cycles

Section 3


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Thermodynamic Cycles

Air-standard analysisis used to perform elementary analysesof IC engine cycles.

Simplifications to the real cycle include:

1) Fixed amount of air (ideal gas) for woring fluid

!) Com"ustion process not considered

#) Intae and exhaust processes not considered

$) %ngine friction and heat losses not considered

&) Specific heats independent of temperature

'he two types of reciprocating engine cycles analyed are:

1) Spar ignition *tto cycle!) Compression ignition +iesel cycle


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SI Engine Cycle vs Thermodynamic Otto Cycle

,

I -

Com"ustion

roducts

Ignition

Intake

Stroke

F/%0

Fuel,ir

2ixture

,ir

'C

3C

Compression

Stroke

Power

Stroke

Exhast

Stroke

!in !ot

Compression

Process

Const volme

heat addition

Process

Expansion

Process

Co

nst volme

heat re"ection

Process

,ctual

Cycle

*ttoCycle


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Actal SI Engine cycle

TC #C

Ignition


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rocess 1! Isentropic compressionrocess !# Constant 4olume heat addition

rocess #$ Isentropic expansion

rocess $1 Constant 4olume heat re5ection

v2

TC

TCv1

#C

#C

Qout

Qin

Air-Standard Otto cycle

3

4

2

1

v

v

v

vr ==

Compression ratio:


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$irst %aw Analysis o& Otto Cycle

1! Isentropic Compression

)()( 12m

W

m

Quu in=

2

1

1

2

1

2

vv

TT

PP =

,I-

)()( 1212 TTcuum

Wv

in ==

!# Constant 6olume 7eat ,ddition

m

W

m

Q

uu in

+= )()( 23

)()( 2323 TTcuum

Qv

in ==

2

3

2

3

T

T

P

P=

,I- Qin'C

11

2

1

1

2 =

= k

k

rv

v

T

T


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#$ Isentropic %xpansion

,I-)()( 34m

W

m

Quu out+=

)()( 4343 TTcuum

Wv

out ==

4

3

3

4

3

4

v

v

T

T

P

P =

$1 Constant 6olume 7eat -emo4al

,I- Qoutm

W

m

Quu out = )()( 41

)()( 1414 TTcuum

Qv

out ==

1

1

4

4

T

P

T

P =

3C

1

1

4

3

3

4 1

=

=

k

k

rv

v

T

T


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( ) ( )( )23

1243

uu

uuuu

Q

W

in

cycle

th == ( ) ( )

23

14

23

1423 1uu

uu

uu

uuuu

=

=

Cycle thermal efficiency:

thin

thincycle

r

r

u

mQ

kr

r

VP

Q

P

imep

VV

Wimep

=

=

=

1

/

1

1

1 111121

Indicated mean effecti4e pressure is:

8et cycle wor:

( ) ( )1243 uumuumWWW inoutcycle ==

$irst %aw Analysis Parameters

1

2

1

23

14 111)(

)(1 ==

=

k

v

v

rT

T

TTc

TTc


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E&&ect o& Compression 'atio on Thermal E&&iciency

Spar ignition engine compression ratio limited "y '#(autoignition)

and #(material strength)9 "oth r

For r; < the efficiency is &=> which is twice the actual indicated 4alue

'ypical SI

engines

? @ r@ 11

; 1.$

1

11 = k

const cth

rV


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E&&ect o& Speci&ic (eat 'atio on Thermal E&&iciency

1

11 = k

const cth

rV

Speci&ic heat

ratio )k*

Cylinder temperatures 4ary "etween !AB and !AAAB so 1.! @ @ 1.$

; 1.# most representati4e


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'he net cycle wor of an engine can "e increased "y either:

i) Increasing ther(1!)ii) Increase Qin(!#D)

6! 61

QinWcycle

1

!

#

(i)

$

(ii)

$actors A&&ecting +ork per Cycle

1

$

$

#th

incycle

r

r

V

Q

VV

Wimep

=

=1

121


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E&&ect o& Compression 'atio on Thermal E&&iciency and ,EP

=

k

in

rr

r

VP

Q

P

imep 11

1111

k ./3


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Thermodynamic Cycles &or CI engines

In early CI engines the fuel was in5ected when the piston reached 'C

and thus com"ustion lasted well into the expansion stroe.

In modern engines the fuel is in5ected "efore 'C (a"out 1&o)

'he com"ustion process in the early CI engines is "est approximated "y

a constant pressure heat addition process 0iesel Cycle

'he com"ustion process in the modern CI engines is "est approximated

"y a com"ination of constant 4olume and constant pressure 0al Cycle

$el in"ection starts$el in"ection starts

Early CI engine ,odern CI engine


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Early CI Engine Cycle and the Thermodynamic 0iesel Cycle

,

I -

Com"ustion

roducts

Fuel in5ected

at 'C

Intake

Stroke

,ir

,ir

3C

Compression

Stroke

Power

Stroke

Exhast

Stroke

!in !ot

Compression

Process

Const pressre

heat addition

Process

Expansion

Process

Const volme

heat re"ection

Process

,ctual

Cycle

+ieselCycle


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rocess 1

! Isentropic compressionrocess !# Constant pressure heat addition

rocess #$ Isentropic expansion


Air-Standard 0iesel cycle

Qin

Qout

2

3

v

vrc=

CutEoff ratio:

v2

TC

v1

#CTC

#C


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( )

m

VVP

m

Quu in 23223 )()(

+=

,I-!# Constant ressure 7eat ,ddition

)()( 222333 vPuvPum

Qin ++=

)()( 2323 TTchhm

Qp

in ==

crv

v

T

T

v

RT

v

RTP ====

2

3

2

3

3

3

2

2

Qin

$irst %aw Analysis o& 0iesel Cycle

%uations for processes 1!9 $1 are the same as those presented

for the *tto cycle


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)()( 34m

W

m

Quu out+=

,I-

#$ Isentropic Expansion

)()( 4343 TTcuum

Wv

out ==

note v4=v

1so

cr

r

v

v

v

v

v

v

v

v

v

v===

3

2

2

1

3

2

2

4

3

4

r

r

T

T

P

P

T

vP

T

vP c==3

4

3

4

3

33

4

44

11

4

3

3

4

=

=

k

c

k

rr

vv

TT


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23

1411hh

uu

mQ

mQ

in

out

cycleDiesel

==

( )

( )

=

1

1111

1

c

kc

k

const c

Diesel

r

r

krV

For cold airEstandard the a"o4e reduces to:

Thermal E&&iciency

1

11 = kOtto

r

recall9

8ote the term in the suare "racet is always larger than one so for the

same compression ratio9 r9 the +iesel cycle has a lowerthermal efficiency

than the *tto cycle

8ote: CI needs higher r compared to SI to ignite fuel


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'ypical CI %ngines

1& @ r@ !A

Ghen rc(; 4#4!)1 the +iesel cycle efficiency approaches the

efficiency of the *tto cycle

Thermal E&&iciency

7igher efficiency is o"tained "y adding less heat per cycle9 H in9

run engine at higher speed to get the same power.


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k ./3

k ./3

'he cutEoff ratio is not a natural choice for the independent 4aria"le

a more suita"le parameter is the heat input9 the two are related "y:

111

11

1

= kin

c rVP

Q

k

k

ras Q

in

0, rc

1


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rocess 1! Isentropic compression

rocess !!.& Constant 4olume heat addition

rocess !. Constant pressure heat additionrocess #$ Isentropic expansion


0al Cycle

Qin

Qin

Qout

..

1

1

1/2

1/2

3

3

)()()()( 5.2325.25.2325.2 TTcTTchhuu

m

Qpv

in +=+=


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Thermal E&&iciency

)()(

115.2325.2

14

hhuu

uu

mQ

mQ

in

out

cycle

Dual

+

==

( )

+

= 1)1(

111

1 c

k

c

kcconst

Dualrk

r

rv

1

11 = kOtto r

( )( )

= 1111

11

c

kc

kconst cDiesel

r

r

krV

8ote9 the *tto cycle (rc;1) and the +iesel cycle (;1) are special cases:

2

3

5.2

3 andwhereP

Pv

vrc ==


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'he use of the +ual cycle reuires information a"out either:

i) the fractions of constant 4olume and constant pressure heat addition

(common assumption is to equallysplit the heat addition)9 orii) maximum pressure #.

'ransformation of rcand into more natural 4aria"les yields

= 11111 1

11 krVPQ

kkr kinc

1

31PP

rk=

For the same inlet conditions 19 61and the same compression ratio:

DieselDualOtto

>>

For the same inlet conditions 19 61and the same pea pressure #

(actual design limitation in engines):

ottoDualDiesel >>


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For the same inlet conditions 19 61

and the same compression ratio P2/P1:For the same inlet conditions 19 61

and the same peak pressure P3:

=

=

32

141

1

Tds

Tds

Q

Q

in

outth

+iesel

+ual

*tto

+iesel+u

al*tto

xD J!.&D

max

'max

o

o

Pressre4

P

Pressre4

P

Temperatre4

T

Temperat

re4

T

Speci&ic 5olme

Speci&ic 5olme

Entropy Entropy


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$inite (eat 'elease ,odel

In the *tto cycle it is assumed that heat is released instantaneously.

, finite heat release model specifies heat release as a function of cran

angle.

'he cumulati4e heat release or 6rn &ractionxbis gi4en "y:

=

n

d

sb ax

exp1)(

where ; cran angles; start of heat release

d; duration of heat release

n; form factora; efficiency factor

/sed to fit to experimental data

A @ xb@ 1


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$inite (eat 'elease

, typical heat release cur4e consists of an initial spar ignition phase9

followed "y a rapid "urning phase and ends with "urning completion phase

'he cur4e asymptotically approaches 1 so the end of com"ustion is defined

"y an ar"itrary limit9 such as ?A> or ??> complete com"ustion wherexb; A.?A or A.?? corresponding 4alues for efficiency factor aare !.# and $.=

'he rate of heat release as a function of cran angle is:

( )

==

1

1

n

d

sb

d

inb

in xna

Q

d

dxQ

d

dQ

bindxQdQ=

/77


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( )

+=

+=

+=

==

=

d

dQ

V

k

d

dV

V

P

kd

dP

d

dPV

d

dVP

R

c

d

dVP

d

dQ

VdPPdVR

cPdVQ

mR

PVdmcdTmcdU

WQdU

d

v

v

vv

1

anglecrankunitper

gasidealassuming

changeanglecranksmalla!or

c"linderin thegasthecontainings"stemclosedtheto#aw$irst%ppl"ing



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'he cylinder 4olume in terms of cran angle9 V(!is

( )2122 )sin(cos121)( ++= RRVrVV dd

+ifferentiating wrt

( )2122 )sin(cos1sin2

+=

RV

d

dV d

where

slR

r

"#Vd

2

rationcompressio

nt &olumedisplaceme4

2

=

=

==

For the portion of the compression and expansion stroes with no heat

release9 where sand ! s" ddQ$d'



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$inite (eat 'elease ,odel 'eslts

Start o& heat release8

Engine . - 19o6TC

Engine 1 - TC

0ration 9o


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$inite (eat 'elease ,odel 'eslts

[Flip-Side] 3. Thermodynamic Cycles

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