Gas Turbine Power Plants Gas Turbine Power Plants are lighter and more compact than vapor power plants. The favorable power-output-to- weight ratio for gas turbines make them suitable for transportation.

Air-standard Brayton Cycle

188

For steady-state: )(0 outinCVCV hhm

Wm

Q−+−=

&

&

&

&

1 2 Adiabatic compression )( 12 hhm

in −=&

&W

2 3 Heat addition )( 23 hhm

Qin −=&

&

3 4 Adiabatic expansion )( 43 hhmout −=&

&W

4 1 Heat removal )( 14 hhm

Qout −=&

&

Cycle Thermal Efficiency:

23

1411hhhh

mQmQ

in

out

cycleBrayton −

−−=−=

&&&&

η

Back work ratio:

43

12

hhhh

mWmWbwr

out

in

−−

==&&&&

189

Ideal Air-standard Brayton Cycle (processes are reversible) 1 2 Isentropic compression 2 3 Constant pressure heat addition 3 4 Isentropic expansion 4 1 Constant pressure heat removal

Qin

Qout

For the isentropic process 1 2

=

1

212 P

PPP rr

For the isentropic process 3 4

=

3

434 P

PPP rr

190

Ideal Cold Air-standard Brayton Cycle For isentropic processes 1 2 and 3 4

k

k

PP

TT

1

1

2

1

2

−

= and

kk

PP

TT

1

3

4

3

4

−

=

Since 4

3

1

2

PP

PP

= thus 4

3

1

21

4

31

1

2

TT

TT

TT

TT k

kkk

=→

=

−−

Thermal Efficiency

( )( )

( )( )1/

1/111232

141

23

14

23

14

−−

−=−−

−=−−

−=TTTTTT

TTcTTc

hhhh

P

P

constkBraytonη

recall 2

3

1

4

4

3

1

2

TT

TT

TT

T=→=

T

( ) kk

constkBrayton

PPTT

1

122

1 111 −−=−=η

191

Efficiency increases with increased pressure ratio across the compressor

Back work ratio

( ) 43

12

43

12 )(TTTT

TTcTTc

mWmW

mWmWbwr

P

P

turb

comp

out

in

−−

=−−

===&&

&&

&&&&

Typical BWR for the Brayton cycle is 40 - 80% compared to < 5% for the Rankine cycle. Recall, reversible compressor work is given by ∫

21 vdP

Since gas has a much larger specific volume than liquid much more power is required to compress the gas from P1 to P2 in the Brayton cycle compared to the Rankine cycle for which liquid is compressed. The turbine inlet temperature is limited by metallurgical factors, e.g., Tmax = 1700K

192

Gas Turbine Irreversibilities In the ideal Brayton cycle all 4 processes are assumed reversible, thus processes 2-3 and 4-1 are constant pressure and processes1-2 and 3-4 are isentropic. The constant pressure assumption does not normally incur any great errors but the compressor and turbine processes are far from isentropic

Ideal (reversible) processes: 1 - 2s and 3 - 4s

Actual (irreversible) processes:

1 - 2 and 3 - 4

These irreversiblities are taken into account by:

s

s

t

t

turb hhhh

mW

mW

43

43

−−

=

=

&&

&&

η 12

12

hhhh

mW

mW

s

c

s

c

comp −−

=

=

&&

&&

η

193

Efficiency versus Power Consider two Brayton cycles A and B with a similar turbine inlet temperatures T3

Since BA P

PPP

>

1

2

1

2 BA ηη >

Since (enclosed area 1-2-3-4)B > (enclosed area 1-2-3-4)A

A

cycle

B

cycle

mW

mW

>

&

&

&

&

Bcycle

Acycle

B

A

WW

mm

,

,&

&

&

&=

In order for cycle A to produce the same amount of net power as cycle B, i.e., BcycleAcycle WW ,,

&& = , need BA m&& >m . Higher mass flow rate requires larger (heavier) equipment which is a concern in transportation applications

194

Increasing Cycle Power The net cycle power is: ctcycle WWW &&& −= The cycle power can be increased by either increasing the turbine output power or decreasing the compressor input power. Gas Turbine with Reheat The turbine work can be increased by using reheat, as was shown in the Rankine cycle

2 3 a b

Compressor

1 4

The turbine is split into two stages and a second combustor is added where additional heat can be added

195

Recall: '4

3

1

2

TT

TT

= so, isobars on T-s diagram diverge

Note:

&2,inQ&

The tot

The tot

W

Since h

Since t

The rehadditio

T

Q 1,in

al turbine work out([ hWbasic

&3=

al turbine work outWW tt

reheatwturbine

&&&,1,

/+=

b - h4 > ha - h4’

he compressor work

rewcycleW&

/

eat cycle efficiencynal heat Q is add2,in

&

3

hb - h4 > ha - h4’

2

1

p−

p2

W

h

a

ut witho) (hha +

ut with ([ h3 −=

reheatwturbine&

/

h2 - h1 i

bc

eatW&>

is not ned betw

b

4

r

s

ay

ee

s

4’

ut reheat is: )]mha &'4−

eheat is: ) ( )]mhhh ba &4−+

basicW&>

unaffected by reheat

siccle

cessarily higher since en states a and b

196

Compression with Intercooling The compressor power can be reduced by compressing in stages with cooling between stages.

Recall:

'4

3

1

2

TT

TT

= so, isobars on T-s diagram diverge

d

2’

h2’ – hc > h2 – hd

2’

197

The compressor power input without intercooling is:

( ) ( )[ ]mhhhhW ccbasic &&1'2 −+−=

The total compressor power input with intercooling is:

( ) ( )[ ]mhhhhWWW dcccreheatw

comp &&&& −+−=+= 212,1,/

Since h2’ – hc > h2 – hd basic

reheatwcomp WW && <

/

Since the turbine work h3 – h4 is unaffected by intercooling

basiccycle

reheatwcycle WW && >

/

198

Different approach: The reversible work per unit mass for a steady flow device is ∫ vdP , so

Without intercooling : mWc

&

&

With intercooling : mW

w

c

&

&

Since area(b-1-c-2’-a) > ar

basi

c

mW

&

&

2’

-a-c-b-

vdPvdPvdPc

c

basic

'21 area

'22

1 1

=

∫∫ ∫ +==

-a-c-d-b-

vdPvdPvdPd

c

/

21area

22

1 1int

=

∫∫ ∫ +==

ea(b-1-c-d-2-a)

int/w

c

c mW

>&

&

199

Aircraft Gas Turbines Gas turbine engines are widely used to power aircraft because of their high power-to-weight ratio Turbojet engines used on most large commercial and military aircraft

Ideal air-standard jet propulsion cycle:

NozzleDiffuser 3

541

2

a

200

Normally compression through the diffuser (a-1), and expansion through the nozzle (4-5) are taken as isentropic

&

In the ideal jet propulsioto ambient pressure Pa. Instead the gas expands such that the power prodcompressor, no net cyclethus

( 2h −

After the turbine the gaswhich is the same as Pa.

inQ

&

n eng

to an uced pow

)

mWc =&

&

1h =

expan

outQ

ine the gas is not expanded

intermediate pressure P4 is just sufficient to drive the er produced ( 0=cycleW& ),

(

mWt

&

&

)43 hh −

ds to ambient pressure P5

201

Apply the steady-state conservation of energy equation to the Diffuser and Nozzle

+−

++−=

220

22out

outin

inCVCV VhVhm

Wm

Q&

&

&

&

Diffuser slows the flow to a zero velocity relative to the engine:

Diffuser (a 1)

kconstant for 2

2

22

2

1

2

1

221

1

P

aa

aa

aa

cVTT

Vhh

VhVh

+=

+=

+=+

Nozzle accelerates the gas leaving the turbine (turbine exit velocity negligible compared to nozzle exit velocity):

Nozzle (4 5) ( )

( ) kconstant for 2

222

545

545

25

5

24

4

TTcV

hh

VhVh

P −=

−=

+=+

V

202

The gas velocity leaving the nozzle is much higher than the velocity of the gas entering the diffuser, this change in momentum produces a propulsive force, or thrust Ft

( )at VVmF −= 5& Where V is flow velocity relative to engine For aircraft under cruise conditions the thrust just overcomes the drag force on the aircraft fly at high altitude where the air is thinner and thus less drag To accelerate the aircraft increase thrust by increasing V5 In military aircraft afterburners are used to get very large thrust for short take-offs on aircraft carriers

An afterburner is simply a reheat device!

203

Other Propulsion Systems

Turboprop

Subsonic ramje

In turbofan bypass flow produces additake-off. During cruise thrust comes fr In a ramjet engine there is no compresscompression is achieved gasdynamical Ramjet engines produce no thrust whemust be coupled with a turbojet engineground

Turbofan

t

tional thrust for om turbojet

or or turbine, ly.

n stationary thus to get off the

204

Supersonic Ramjet Engine The flow is decelerated to subsonic velocity before the burner via a series of shock waves. Combustion occurs at constant pressure

Supersonic exhaust flow

T

Supersonic free stream flow

choked flow

urbojet-ramjet combination:

205

Supersonic Combustion Ramjet (SCRAMJET) Engine At very high Mach numbers the air temperature gets extremely hot after deceleration through the diffuser

2

2

1P

aa c

VTT +=

For Mach 6 flight speed, the air temperature just before the burner reaches about 1550K. At this temperature the air dissociates resulting in a drop in enthalpy At flight speeds greater than Mach 6 (hypersonic) better to burn fuel- in supersonic air stream

206

US National Aero Space Plane (X-30)

Was to use 5 scramjet engines to achieve a Mach 12 flight speed To be used for travel to space and also as an airliner, a flight between any two points on earth would take less than 2 hours Canceled in 1993! Several countries have similar planes on the drawing board, Canada is not one of them!

207