Gas turbine efficiency - 7th January 2010

Gas Turbine
IdealIdeal
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
efficiency
0.4
γ
η 1
1
1 −
−=simple
Gasturbineefficiency
0.2
0.3
γ
γ
η 1
2
1 −






−=
P
P
simple
Gasturbine
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 ratio
Overallgasturbineefficiency
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)
compressor fitted with
recuperator)
Capstone C65
(with recuperator)
( )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.
efficiency
0.4
to irreversible losses.
0.3
Gasturbine
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%
Recuperator
Clearly, recuperator helps to increase
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

GasturbineefficiencyGasturbineefficiency
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. LMpressure 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 = 3
η
1
−=
γ 1−
3T
t =
Heat-exchange cycle
0.7
0.8
0.9
t = 3
t = 3.5
t = 4
t = 4.5
t = 5
Simple cycleγ
γ
η 1
1
2
1
1 −






−=
P
P
simple
t
P
P
exchangeheat
γ
η 1
2
1






−=−
1
3
T
T
t =
0.5
0.6
0.7
Braytoncycleefficiency
t = 5
t = 5.5
Heat-exchange
cycle
0.3
0.4
0.5
0.1
0.2
0.3
0.0
0.1
0 5 10 15 20 25 30 35 40 45
Pressure 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
T
exchangeheat −=ηWhen (P2/P1) = 1
0.7
0.8
0.9
t = 3
t = 3.5
t = 4
t = 4.5
t = 5
Simple cycle
This is called Carnot efficiency
0.5
0.6
0.7
t = 5
t = 5.5
Heat-exchange
cycle
0.3
0.4
0.5
0.1
0.2
0.3
0.0
0.1
0 5 10 15 20 25 30 35 40 45
Pressure ratio

Carnot cycle (from Wikipedia)Carnot cycle (from Wikipedia)
3
1
_ 1
T
T
exchangeheat −=η
3

Heat-exchange cycle
0.9
t = 2
Simple cycle
t = 2.5
t = 3
Heat-exchange cycle
3
1
_ 1
T
T
exchangeheat −=ηWhen (P2/P1) = 1
Question:
0.7
0.8
0.9
t = 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
t = 5
t = 5.5
Heat-exchange
cycle
built for pressure ratio of one?
0.3
0.4
0.5
0.1
0.2
0.3
0.0
0.1
0 5 10 15 20 25 30 35 40 45
Pressure ratio

Heat-exchange cycleHeat-exchange cycle
2.00
Specific work output vs pressure ratio
T3/T1 = 2
1.50
Specific work output vs pressure ratio
T3/T1 = 2
T3/T1 = 3
T3/T1 = 4
T3/T1 = 5
1.00
Specificworkoutput[W/(Cp*T_in)]
0.50
Specificworkoutput[W/(
0.00
0 5 10 15 20 25 30
Specificworkoutput[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
5
6
fuel fuel
1
3
5

Reheat cycle
0.9
Simple cycle
t = 2.5
t = 3
t = 3.5
η
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 cycle
γ
γ
η 1
1
2
1
1 −






−=
P
P
simple
c
c
t
t
c
c
t
t
reheat
−−
+−−
=
2
1
2
2
η
γ
γ 1
1
2
−






=
P
P
c
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 io

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
c
c
t
t 1
2
2 +−−
=η
Reheat + heat-exchange cycle
γ
γ
η 1
2
1
1 −




−=
P
simple
0.7
0.8
t = 3.5
t = 4
t = 4.5
t = 5
t = 5.5
t = 2
c
t
t
c
exchangeheatreheat
2
2 −
=−+η
Simple 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 io

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 efficiencypressure 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’sefficiency 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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