thermodynamica 1 - tu delft ocw · march 15, 2010. 1. thermodynamica 1. lecture 11: processtappen....

March 15, 2010

1

Thermodynamica 1

Lecture 11: ProcesstappenKringprocessen

• Stirling• Otto (2 en 4 slags)

Bendiks Jan BoersmaWiebren de JongThijs VlugtTheo Woudstra

Energy Technology

Energy Technology

Lecture 11, March 15, 2010 2

Recap College 10• Carnot process• working with the entropy

• Carnot process

2 isothermal and 2 adiabatic processesreversible isentropic=adiabatic

Carnotreal

h

cCarnot T

TTT

114

3

Stirling cycle

3

Energy Technology

Efficiency Stirling cycle


pTpT

pTpT

vvRTTcT

vvRTTcT

vvvvTTTT

vvRTTTcTTcvvRT

QQQQ

QQ

QW

h

c

v

v

v

v

in

uit

in

11

)/ln()()/ln(

)(

1

//)isothermenzijn 4-3en 2-(1

)/ln()()()/ln(111

3

1

43

233

21

141

4312

2314

43332

14211

3423

4112

Energy Technology

Stirling met regenerator


1 2 1 2 1

3 4 3 4 3

4 1 3 2

2 1 3 4

1

3

| | | | | ln ( / ) |1 1 1ln ( / )

(1 -2 en 3 -4 z ijn iso th e rm en )/ /

1 1 M et reg en e ra to r d u s C a rn o t!

u it

in in

c

h

Q Q R T v vWQ Q Q R T v v

T T T Tv v v v

TTT T

2341 d toegevoersysteemhet aan weer regenrator wordt via QQ

Energy Technology


Verbrandingsmotoren bv Otto motor

2 adiabaten en 2 isochoren, dus geen Carnot machine

en Carnot cyclus!

Energy Technology


Standaardlucht aannames (air standard):

• Werkmedium: lucht als ideaal gas• Kringproces is gesloten• Deelprocessen zijn inwendig reversibel• Warmtetoevoer i.p.v. verbrandingsprocessen• Warmteafvoer i.p.v. uitdrijfproces

2

2 112

2 1 2 11

; ( )

( )

p

p p p

p p

dh c dT

h h c dT c c T

h h c dT c T T

Gebruik dus tabel A-22

Energy Technology


Koude lucht aannames (cold air standard):

• Werkmedium: lucht als ideaal gas, Cp en Cv zijn constant• Kringproces is gesloten• Deelprocessen zijn inwendig reversibel• Warmtetoevoer i.p.v. verbrandingsprocessen• Warmteafvoer i.p.v. uitdrijfproces

2

2 1 2 11

( )

p

p p

dh c dT

h h c dT c T T

Gebruik dus geen tabel

Energy Technology


Ideal gas (cold air standard)

1 *

1 11 1 2 2

11

1 2 1

2 1 2

1 **

11 1

2 2

/

/

P V C onstT V C onst

P m R T V

T V T V

T V VT V V

P V C onstP T C onst

V m R T P

P TP T

Energy Technology


Isentroop process (example 6.9)

1

1

2

2

2 2 2

1 1 1

2 1/( 1) 1.39 /.39

2 2 2

1 1 1

1300650?

21.86Air Standard: ( 22)1.3860

15.77 15.77

650Cold air Standard: 15.81300

r

r

k k

p barT KT Kp

p p pT Ap p p

p p bar

p T p barp T p

Energy Technology


Recap: reversible process steps in closed systems

isotherm (T=const.)

isochor (v=const.)

isobar (p=const.)

adiabatic (dQ=0)

polytropic(pvn=const.)

W12 2

1

v

vdvpmQ12

1

2

1

2 lnlnvvRT

ppRT QW 1212

0

0

121 vvpm

12 uum

11221vpvp

nm

12

2

1

uumdTcmT

Tv

12

2

1

hhmdTcmT

Tp

Wuum 1212

ideal gas ideal gas

Energy Technology


Recap: reversible process steps in closed systems

isotherm (T=const.)

isochor (v=const.)

isobar (p=const.)

adiabatic (dQ=0)

polytropic(pvn=const.)

W12Q12p

V

W121

2

T

S

Q121

2 pvp

V

2

1

T

S

1

2

p

V

W121

2

p

V

1

2

for 1>n>kW12T

S

1

2 Q12

for 1>n>k

T

S

Q1212

pv

p

V

21 W12

T

S

Q12

1 2

T1T2

T2

T1

012 Q

012 W

Energy Technology


Common combustion engines

•Otto

•Diesel

•Gasturbine

Energy Technology


.

NOx- emission and efficiency of combustion engines

Energy Technology


Q23

Q41

Recap: Otto cycleT

S

p

V

2

1 T1

3

4 T4 1

2

p

v

4

3

2323 uumQ 023 W

4141 uumQ 041 W

012 Q

034 Q

1212 uumW

3434 uumW

internally reversible processes1-2

adiabatic

compression

of the air as the piston moves from

bottom

dead

center to top dead

center

2-3

isochoric

heating

of air from

external

source

–

to mimic

the ignition

and oxidation

of fuel-air

mixture

3-4

power stroke: adiabatic

expansion

4-1

isochoric

heat transfer

to external

reservoir –

to mimic

the release of hot exhaust

Energy Technology


Efficiency Otto cycle (cold air standard)

thermal efficiency

Poisson relation

3241 , VVVV

1 .k

p

v

TV constc

kc

1

2

1

1

2

k

VV

TT

2 1 4 312 34 4 1

23 23 3 2 3 21

cycrev u u u uW W u uW

Q Q u u u u

1

2

1

2

1

1

3

4

4

3

TT

VV

VV

TT

kk

4 1 1 4 1 1

3 2 2 3 2 2

4

3

11 1 1

1

=1-

vrev

v

c T T T T T Tc T T T T T T

TT

1

4

2

3

TT

TT

Energy Technology


rev

21 VVr

Efficiency Otto cycle (cold air standard)

thermal efficiency

with compression ratio 1

2

VrV

4 1 1

3 2 2

( )1 .. 1( )

rev v

v

C T T TC T T T

11

1

2

2

1

k

TT

VVrkpV const

.1 constTV k

1

11revkr

1 5 10

Energy Technology


The efficiency monotonically increases with the compression ratio

in practice, high compression ratios leads to high temperatures, resulting{1} in NOx emissions (oxidation of air-nitrogen, severe at T>1600 K){2} in “knock”, the spontaneous ignition of air-fuel mixture prior to spark plug{3} incomplete combustion

compression ratios of r10 are therefore common (efficiency <60%)

1

11revkr

Energy Technology


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16

Compressie verhouding, r [-]

Ren

dem

ent [

-]

Mas

erat

i Qua

trop

orto

3.2

(ren

d.=0

.41;

247

kW

)

Pors

che

Car

rera

(ren

d.=0

.50;

235

kW

)

Lam

borg

ini M

urci

elag

o (r

end.

=0.4

5; 4

26 k

W)

Lotu

s Es

prit

(ren

d.=0

.52;

260

kW

)

Mer

cede

s SL

(ren

d.=0

.50;

350

kW

)

Ope

l Ast

ra 1

.6 (r

end.

=0.2

3; 5

5 kW

)

Volk

swag

en G

olf 1

.6 (r

end.

=0.2

9; 7

7 kW

)Pe

ugeo

t 306

1.6

(ren

d.=0

.29;

80

kW)

Angulo-Brown et al [1994]

9.3

F. Angulo-Brown et al [1994] “ Compression ratio of an optimized air standard Otto-cycle model”, Eur. J. Physics, Vol. 15, pp. 38-42

irreversible processes: heat transfer processes, friction in cylinders and dissipation in cycle, non-isochoric processes

1

11 krev

r

21 VVr

Efficiency Otto cycle

irrev

Energy Technology


1=5

4

3

2

dual cycle

6

4-stroke Otto cycle

Ideal process steps of 4-stroke Otto cycle1-2 adiabatic compression of air (1st stroke)2-3 isochoric heating, to mimic the ignition and oxidation of fuel-air mixture3-4 power stroke: adiabatic expansion (2nd stroke)4-5 isochoric heat transfer, to mimic opening of exhaust valve5-6 exhaust stroke (3rd stroke): isobaric displacement of exhaust gas6-1 intake stroke (4th stroke): isobarically drawing fresh air into the cylinder

p

V

Energy Technology


Dual cycle

1=5

4

3

2

dual cycle

6

4 stroke dual cycle

Energy Technology


34 45 32 51

23 34 23 34

23 3 2

34 4 3

51 5 1

5 14

3 2 4 3

1 1

( )( )

( )

1( )

/

out

in in

v

p

v

tact

p v

W W W Q QWQ Q Q Q Q Q

Q mc T TQ mc T T

Q mc T TT T

T T k T Tk c c

Efficiency of dual cycle

Energy Technology


Tentamen juni 2010We willen een gasmotor gebruiken om 3MW elektriciteit op te wekken. De compressie verhouding van de gasmotor is 12 en het cilinder volume aan het begin van de arbeidsslag is 2 liter. Er is gegeven dat Cp =1.0KJ/kgK en Cv=0.714KJ/kgK en dat de laagste druk in het systeem gelijk is aan 1 bar

• Schets het p-v en T-s diagram voor de Otto cyclus. • Bepaal het volume V1, als gegeven is dat T1=300K bepaal dan T2.• Tijdens het proces 23 neemt de druk in de motor toe met een factor 2.5.• Hoe groot zijn dan T3 en T-4?• Bepaal de warmte toe en afvoer aan het systeem Q23 en Q41?• Bepaal de geleverde arbeid en het rendement van de motor

thermodynamica 1 - tu delft ocw · march 15, 2010. 1. thermodynamica 1. lecture 11: processtappen....

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