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
TURBO GROUP – Gas turbine ideal efficiency
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
4Gas turbine ideal efficiency
Compression ratio
TURBO GROUP – Gas turbine ideal efficiency
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
TURBO GROUP – 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
Gas turbine ideal efficiency
Compression ratio
TURBO GROUP – Gas turbine ideal efficiency
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
7Gas turbine ideal efficiency
Compression ratio
TURBO GROUP – Gas turbine ideal efficiency
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
8Gas turbine ideal efficiency
Compression ratio
TURBO GROUP – Gas turbine ideal efficiency
Heat-exchange cycleHeat-exchange cycle
9Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
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.
Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
Heat-exchange cycle
Brayton cycle efficiency vs pressure ratio
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
11Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
Carnot cycle (from Wikipedia)Carnot cycle (from Wikipedia)
3
1
_1
T
Texchangeheat −=η
3
12Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
Heat-exchange cycle
Brayton cycle efficiency vs pressure ratio
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
13Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
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.
14Gas turbine ideal efficiency
Pressure ratio
TURBO GROUP – Gas turbine ideal efficiency
Reheat cycleReheat cycle
1
2 4
56
fuel fuel
13
5
15Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
Reheat cycle
Brayton cycle efficiency vs pressure ratio
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
16Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
Reheat with heat-exchange cycleReheat with heat-exchange cycle
17Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
Reheat with heat-exchange cycleReheat with heat-exchange cycle
Brayton cycle efficiency vs pressure ratio
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
18Gas turbine ideal efficiency
TURBO GROUP – Gas turbine ideal efficiency
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 ideal efficiency
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