gas turbine efficiency - 7th january 2010

Gas Turbine

Ideal Ideal

Efficiency

7th January 2010

Prepared by: Cheah CangTo

TURBO GROUP – Gas turbine ideal efficiency

Olympus turbojet engine (Rolls-Royce)

Objective of this discussion is to introduce ideal gas turbine efficiency for:

a) Simple cycle

b) Heat-exchange (recuperator) cycleb) Heat-exchange (recuperator) cycle

c) Reheat cycle

d) Reheat with heat-exchange cycle

2Gas turbine ideal efficiency


Simple cycleSimple cycle



Simple cycle

0.7

Simple cycle

0.5

0.6

eff

icie

ncy

0.4

γη

1

11

−−=simple

Gas t

urb

ine e

ffic

ien

cy

0.2

0.3γ

γη

1

2

1−

−=

P

P

simple

Gas t

urb

ine

0.1

0.2

1

P

0.0

0 5 10 15 20 25 30 35 40

Compression ratio

Note: γγγγ = 1.4 for ambient air


Compression ratio


Actual GT efficiency vs pressure ratio

Overall GT efficiency versus compression ratioO

vera

ll g

as t

urb

ine e

ffic

ien

cy

Rolls-Royce 501-KH5

(steam injected)Capstone C200, C600, C800

and C1000 (all engines are

single wheel centrifugal

compressor fitted with

Solar Mercury 50

(with recuperator)

Overa

ll g

as t

urb

ine e

ffic

ien

cy

compressor fitted with

recuperator)

Capstone C65

(with recuperator)

Overa

ll g

as t

urb

ine e

ffic

ien

cy

( )rationcompressiooverall _ln09979.007641.0 ×+=η

(with recuperator)

MAN Turbo AG THM1304-10

(simple cycle)

( )rationcompressiooverall _ln09979.007641.0 ×+=η

Note: Overall GT efficiency is derived from machine manufacturers’ published heat rate..

MAN Turbo AG

MAN Turbo AG

THM1203A (MD)

Compression ratio

Gas turbine heat rate data courtesy of James Bryan [GSGnet.net (2009)]Dresser Rand KG2-3E

MAN Turbo AG

THM1203A (EG)

5

Compression ratio

Gas turbine ideal efficiency


GT thermal efficiency versus pressure ratio: comparison between Brayton and actual cycle

0.6

0.7

0.5

0.6

Brayton

Actual

Reduction of thermal efficiency due to irreversible losses.

eff

icie

ncy

0.4

to irreversible losses.

Gas t

urb

ine e

ffic

ien

cy

0.3Gas t

urb

ine

0.1

0.2

0.0

0.1

6

0 5 10 15 20 25 30 35 40


Compression ratio


THM1304-10 (MANTurbo AG)

Without recuperatorWithout recuperator

PR = 10, Heat rate = 12330 kJ/kW.hr

9.3%

Gas t

urb

ine e

ffic

ien

cy

Recuperator

Clearly, recuperator helps to increase

Gas t

urb

ine e

ffic

ien

cy

Clearly, recuperator helps to increase thermal efficiency for Mercury 50 at nearly identical pressure ratio as THM1304-10.

In this case, 9.3% of efficiency increased between Mercury 50 and THM1304-10.

Mercury 50 (Solar)

PR = 9.9, Heat rate = 9351 kJ/kW.hr

between Mercury 50 and THM1304-10.

Compression ratio


Compression ratio


Gas t

urb

ine e

ffic

ien

cy

Gas t

urb

ine e

ffic

ien

cy

From previous slide, we learned that gas turbine which is equipped with recuperator will have

higher thermal efficiency. But WHY GT at higher

pressure ratio doesn’t fit with recuperator? e.g. LM pressure ratio doesn’t fit with recuperator? e.g. LM 6000, LMS 100, etc.

Compression ratio


Compression ratio


Heat-exchange cycleHeat-exchange cycle



Heat-exchange cycle

Brayton cycle efficiency vs pressure ratio

0.9

t = 2

Simple cycle

t = 2.5

t = 3η1

−=γ 1−

3T

t =

Heat-exchange cycle

0.7

0.8

0.9t = 3

t = 3.5

t = 4

t = 4.5

t = 5

Simple cycleγ

γη

1

1

2

11

−

−=

P

P

simple

t

P

P

exchangeheat

γ

η 1

2

1

−=−

1

3

T

Tt =

0.5

0.6

0.7

Bra

yto

n c

yc

le e

ffic

ien

cy

t = 5

t = 5.5

Heat-exchange cycle

0.3

0.4

0.5

Bra

yto

n c

yc

le e

ffic

ien

cy

0.1

0.2

0.3

0.0

0.1

0 5 10 15 20 25 30 35 40 45Pressure ratio

For higher value of pressure ratio, a heat exchanger would cool the air

10

heat exchanger would cool the air leaving the compressor and so reduce the efficiency.



Heat-exchange cycle


0.9

t = 2

Simple cycle

t = 2.5

t = 3

Heat-exchange cycle

3

1

_1

T

Texchangeheat −=ηWhen (P2/P1) = 1 ��

0.7

0.8

0.9t = 3

t = 3.5

t = 4

t = 4.5

t = 5

Simple cycle

This is called Carnot efficiency

0.5

0.6

0.7

Bra

yto

n c

yc

le e

ffic

ien

cy

t = 5

t = 5.5

Heat-exchange cycle

0.3

0.4

0.5

Bra

yto

n c

yc

le e

ffic

ien

cy

0.1

0.2

0.3

0.0

0.1

0 5 10 15 20 25 30 35 40 45Pressure ratio



Carnot cycle (from Wikipedia)Carnot cycle (from Wikipedia)

3

1

_1

T

Texchangeheat −=η

3



Heat-exchange cycle


0.9

t = 2

Simple cycle

t = 2.5

t = 3

Heat-exchange cycle

3

1

_1

T

Texchangeheat −=ηWhen (P2/P1) = 1 ��

Question:

0.7

0.8

0.9t = 3

t = 3.5

t = 4

t = 4.5

t = 5

Simple cycle

Question:Carnot suggests that recuperated gas turbines at pressure ratio of unity have the highest thermal efficiency. Why none of recuperated gas turbine is built for pressure ratio of one?

0.5

0.6

0.7

Bra

yto

n c

yc

le e

ffic

ien

cy

t = 5

t = 5.5

Heat-exchange cycle

built for pressure ratio of one?

0.3

0.4

0.5

Bra

yto

n c

yc

le e

ffic

ien

cy

0.1

0.2

0.3

0.0

0.1

0 5 10 15 20 25 30 35 40 45Pressure ratio



Heat-exchange cycleHeat-exchange cycle

2.00

Specific work output vs pressure ratioT3/T1 = 2

1.50

Specific work output vs pressure ratioT3/T1 = 2

T3/T1 = 3

T3/T1 = 4

T3/T1 = 5

1.00

Sp

ecif

ic w

ork

ou

tpu

t [W

/(C

p*T

_in

)]

0.50

Sp

ecif

ic w

ork

ou

tpu

t [W

/(

0.00

0 5 10 15 20 25 30

Sp

ecif

ic w

ork

ou

tpu

t [W

/(

-0.50

0 5 10 15 20 25 30

Pressure ratio

Answer:Because turbine work output is zero for gas turbine with pressure ratio of unity.


Pressure ratio


Reheat cycleReheat cycle

1

2 4

56

fuel fuel

13

5



Reheat cycle


0.9

Simple cycle

t = 2.5

t = 3

t = 3.5η

1−=

t+−−

2 γ 1−

Reheat cycle

0.7

0.8

t = 3.5

t = 4

t = 4.5

t = 5

t = 5.5

Simple cycleγ

γη

1

1

2

11

−

−=

P

P

simple

cc

tt

cc

tt

reheat

−−

+−−

=

2

12

2

η

γ

γ 1

1

2

−

=

P

Pc

0.5

0.6

t = 2

0.3

0.4

Reheat cycle

0.1

0.2

Reheat cycle is in-efficient compared to simple cycle, reason for this is small temperature drop across LP turbines.

0.0

0 5 10 15 20 25 30 35 40 45

P r e ssur e r a t i o



Reheat with heat-exchange cycleReheat with heat-exchange cycle



Reheat with heat-exchange cycleReheat with heat-exchange cycle


0.9

Simple cycle

t = 2.5

t = 3

t = 3.5

cc

tt 1

22 +−−

=η

Reheat + heat-exchange cycle

γ

γη

1

2

11

−

−=

P

simple

0.7

0.8

t = 3.5

t = 4

t = 4.5

t = 5

t = 5.5

t = 2

c

tt

cexchangeheatreheat 2

2 −

=−+ηSimple cycle1

2

P

P

0.5

0.6

0.3

0.4

0.1

0.2

0.0

0 5 10 15 20 25 30 35 40 45

P r e ssur e r a t i o



Now, we know the reasons why high pressure ratio GT (e.g. LM 6000, LMS 100, etc) doesn’t fit with heat-exchanger or even reheat cycle:etc) doesn’t fit with heat-exchanger or even reheat cycle:

a) Efficiency of heat-exchange cycle intersects with simple cycle efficiency at pressure ratio of 16.72 for t = 5 (i.e. T3 = 1550 K), i.e. simple cycle’s efficiency pressure ratio of 16.72 for t = 5 (i.e. T3 = 1550 K), i.e. simple cycle’s efficiency overtakes heat-exchange’s from pressure ratio 16.72 onwards.

b) Efficiency of reheat + heat-exchange cycle intersects with simple cycle efficiency at pressure ratio of 23.5 for t = 5 (i.e. T3 = 1550 K), i.e. simple cycle’s efficiency at pressure ratio of 23.5 for t = 5 (i.e. T3 = 1550 K), i.e. simple cycle’s efficiency overtakes heat-exchange’s from pressure ratio 23.5 onwards.

c) Simple cycle simply have higher thermal efficiency at higher pressure ratio.

d) Heat-exchange cycle (recuperated engine) is only good for low pressure ratio application (e.g. Mercury 50).

End of note

19

End of note


gas turbine efficiency - 7th january 2010

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