Gas Turbine Power Plants
Gas Turbine Power Plants are lighter and more compact
than vapor power plants. The favorable power-output-toweight ratio for gas turbines make them suitable for
transportation.
Air-standard Brayton Cycle
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Q CV WCV
0

 (hin  hout )
m
m
For steady-state:
12
23
34
41
Win
Adiabatic compression 
 (h2  h1 )
m
Q in
Heat addition 
 (h3  h2 )
m
W out
Adiabatic expansion 
 (h3  h4 )
m
Q out
Heat removal 
 (h4  h1 )
m
Cycle Thermal Efficiency:
 Brayton
cycle
Q out m
h h
 1
 1 4 1
Q in m
h3  h2
Back work ratio:
Win m
h h
bwr 
 2 1
W out m h3  h4
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Ideal Air-standard Brayton Cycle (processes are
reversible)
12
23
34
41
Isentropic compression
Constant pressure heat addition
Isentropic expansion
Constant pressure heat removal
Qin
Qout
For the isentropic process 1 2
P 
Pr 2  Pr 1  2 
 P1 
For the isentropic process 3  4
P 
Pr 4  Pr 3  4 
 P3 
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Ideal Cold Air-standard Brayton Cycle
For isentropic processes 1  2 and 3 4
k 1
 k
T2  P2
  
T1  P1 
Since
and
k
 k 1
T
P2 P3
thus  2 

P1 P4
 T1 
k 1
 k
T4  P4
  
T3  P3 
k
 k 1
T
  3 
 T4 

T2 T3

T1 T4
Thermal Efficiency
 Brayton  1 
constk
h4  h1
c T  T 
T T / T  1
 1 P 4 1  1 1 4 1
h3  h2
c P T3  T2 
T2 T3 / T2  1
T2 T3
T4 T3
recall



T1 T4
T1 T2
 Brayton  1 
constk
T1
 1
T2
1

k 1
P2 P1 k

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Efficiency increases with increased pressure ratio across
the compressor
Back work ratio
Win m W comp m c P (T2  T1 ) T2  T1
bwr 





Wout m Wturb m c P T3  T4  T3  T4
Typical BWR for the Brayton cycle is 40 - 80% compared
to < 5% for the Rankine cycle.
Recall, reversible compressor work is given by 12 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
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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:
turb
Wt 
 m 
  h3  h4
 
h3  h4 s
Wt 
 m 

s
comp
W c 
 m 

 s h2 s  h1



h2  h1
Wc 
 m 


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Efficiency versus Power
Consider two Brayton cycles A and B with a similar
turbine inlet temperatures T3
P 
P 
Since  2    2    A   B
 P1  A  P1  B
Since (enclosed area 1-2-3-4)B > (enclosed area 1-2-3-4)A
 W cycle 
 W cycle 
W cycle , A
m

A

 
 

 m 
 m 
m B W cycle , B

B 
A
In order for cycle A to produce the same amount of net
power as cycle B, i.e., W cycle , A  W cycle , B , need m A  m B .
Higher mass flow rate requires larger (heavier) equipment
which is a concern in transportation applications
194
Increasing Cycle Power
The net cycle power is: W cycle  Wt  W c
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:
T2 T3
so, isobars on T-s diagram diverge

T1 T4'
Q in , 2
3
Q in,1
T
b
Note:
hb - h4 > ha - h4’
a
2
4
4’
1
s
The total turbine work output without reheat is:
Wbasic  h3  ha   ha  h4' m
The total turbine work output with reheat is:
Wturbine  Wt ,1  Wt , 2  h3  ha   hb  h4 m
w / reheat
Wturbine  Wbasic
Since hb - h4 > ha - h4’
w / reheat
Since the compressor work h2 - h1 is unaffected by reheat
Wcycle
w / reheat
 Wcycle
basic
The reheat cycle efficiency is not necessarily higher since
additional heat Q in , 2 is added between states a and b
196
Compression with Intercooling
The compressor power can be reduced by compressing in
stages with cooling between stages.
T2 T3
so, isobars on T-s diagram diverge

T1 T4'
Recall:
2’
2’
h2’ – hc > h2 – hd
d
197
The compressor power input without intercooling is:
Wbasic  h2'  hc   hc  h1 m
The total compressor power input with intercooling is:
Wcomp
 Wc,1  Wc, 2  hc  h1   h2  hd m
w / reheat
Since h2’ – hc > h2 – hd  Wcomp
 Wbasic
w / reheat
Since the turbine work h3 – h4 is unaffected by
intercooling
Wcycle
w / reheat
 Wcycle
basic
198
Different approach: The reversible work per unit mass for
a steady flow device is  vdP , so
2’
2
c
2
 W c 
  vdP   vdP   vdP
 
Without intercooling :  m  basic 1
1
c
 area b-1-c-2' -a
'
2
c
2
 W c 
  vdP   vdP   vdP
 
With intercooling :  m  w/ int 1
1
d
 area b-1-c-d-2-a
Since area(b-1-c-2’-a) > area(b-1-c-d-2-a)
 W c 
 W c 
 
 
 m  basic  m  w / int
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:
Diffuser
a
1
2
3
Nozzle
4
5
200
Normally compression through the diffuser (a-1), and
expansion through the nozzle (4-5) are taken as isentropic
Q in
Q out
In the ideal jet propulsion engine the gas is not expanded
to ambient pressure Pa.
Instead the gas expands to an intermediate pressure P4
such that the power produced is just sufficient to drive the
compressor, no net cycle power produced (W cycle  0 ),
thus
W c Wt

m
m
h2  h1   h3  h4 
After the turbine the gas expands to ambient pressure P5
which is the same as Pa.
201
Apply the steady-state conservation of energy equation to
the Diffuser and Nozzle
2 
Q CV WCV 
Vin2  
Vout
   hout 

0

  hin 


m
m
2  
2 

Diffuser slows the flow to a zero velocity relative to the
engine:
Va2
V12
h1 
 ha 
2
2
Va2
h1  ha 
Diffuser (a  1)
2
Va2
T1  Ta 
for constant k
2c P
Nozzle accelerates the gas leaving the turbine (turbine
exit velocity negligible compared to nozzle exit velocity):
Nozzle (4  5)
V52
V42
h4 
 h5 
2
2
V5  2h4  h5 
V5  2c P T4  T5  for constant k
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
Ft  m
 V5  Va 
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
Turbofan
Subsonic ramjet
In turbofan bypass flow produces additional thrust for
take-off. During cruise thrust comes from turbojet
In a ramjet engine there is no compressor or turbine,
compression is achieved gasdynamically.
Ramjet engines produce no thrust when stationary thus
must be coupled with a turbojet engine to get off the
ground
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
Supersonic
free stream
flow
choked
flow
Turbojet-ramjet combination:
205
Supersonic Combustion Ramjet (SCRAMJET) Engine
At very high Mach numbers the air temperature gets
extremely hot after deceleration through the diffuser
Va2
T1  Ta 
2c P
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