ME 423 - METU | Department of Mechanical Engineering

Report
ME 423
Chapter 8
PREDICTION OF PERFORMANCE OF
SIMPLE GAS TURBINES
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Prediction of Performance of Simple Gas Turbine
• From cycle calculations it is possible to determine the
PRESSURE RATIO ( Rc ) which will give the best overall
efficiency for a given Tmax.
• MASS FLOW RATE (m)to give the most suitable desired
power output.
• After such preliminary calculations, the most suitable
design data for a particular application can be chosen.
• Then, it is possible to design individual components to
give the required operation at the design point.
• That is running at the design speed N*, mass flow rate
m* and pressure ratio R*.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Prediction of Terformance of Simple Gas Turbine
• Then the off-design performance has to be determined
which is the divergence from the design point over the
complete operating range of speed and power output.
• The performance ¢ of the individual components may be
estimated on the basis of the previous experience or
actual experiments. When they are combined in an
engine their operating range is considerably reduced.
• The problem is to find the Operating point (OP) on each
component ¢ when the engine is running at a steady
speed (EQUILIBRIUM).
• The plot of these OP's form the EQUILIBRIUM
RUNNING LINE (ERL).
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Prediction of Performance of Simple Gas Turbine
• For the whole range of operating speeds, it will generate
the EQUILIBRIUM RUNNING DIAGRAM.
• Determining the OP; the power output, thrust and the
SFC can be obtained.
• The Equilibrium Running Diagram indicates the margin of
operation from the surge line (SL) .
• This margin indicates a Margin of stability; indicates if
there is enough margin to operate with adequate
compressor efficiency.
• If the surge line is crossed some action has to be taken to
recover, not to give rise to a failure.
• Ideally the engine should be operated within the region of
maximum possible efficiencies.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Prediction of Performance of Simple Gas Turbine
• Variation of SFC with reduction in power  PART LOAD
PERFORMANCE. This is important while running the GT
at low power settings.
• Poor sfc at part load is the biggest disadvantage of a GT,
especially a vehicular one.
• The effect of ambient conditions on maximum output is
also important,
i.e. high & low Ta and Pa.
• Peak load energy generation:
 Europe: cold days in winter,
 America: hot days in Summer
 for airplanes: Runway length (safety) and
pay load (economics) are affected.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-Design Performance of Simple GT
• Here we will try to analyse a :
a) Single shaft unit delivering shaft power.
b) Free turbine engine - power turbine drives the load.
c) Simple jet engine, where the useful output is from the
propelling nozzle.
• More complex arrangements - two spool engines,
Turbofan & transient performance Chapter 9
• Flow characteristics of a free turbine and propelling
nozzle are similar and impose the same restrictions on
the Gas Generator.
• As a result of this several jet engines have been
converted to Free Turbine Power engine for peak load
electric generation, and marine applications.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Component Characteristics ¢
• Axial compressor ¢ constant speed lines become
vertical so ηc , Rc vs m is plotted.
FIG.1 Compressor Characteristics
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Component Characteristics ¢
• Turbine ¢  do not show a significant variation in ND
speed. Their operating range is usually severely restricted
by another component downstream.
FIG.2 Turbine Characteristics
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-Design Operation of The Single - Shaft GT
• Since inlet and exhaust pressure losses are ignored;
pressure ratio across the turbine is determined by the
compressor pressure ratio and the pressure loss in the
combustion chamber;
ΔP034 = P012 - P032
• The mass flow through the turbine = mass flow through
the compressor - Bleeds + fuel flow;
m3  m1 -mbleed +mf
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
a) Select a constant speed line on the C¢ and choose an
OP on this line thus
.
m T01 P01
;
; c
P01
P02
N/ T01 are selected.
b) The corresponding point on the T¢ is obtained by the
Compatibility of Speed and Flow.
• COMPATIBILITY OF ROTATIONAL SPEED
N
=
T03
Me 423 Spring 2006
N

T01
T01
T03
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
• COMPATIBILITY OF FLOW
.
.
m 3 T03
=
P03
.
m1 T01
P01
*
P01
P
* 02 *
P02
P03
T03
m
* .3
T01
m1
• Here combustion chamber pressure loss
P03/P02 = 1 - Pb/P02
.
•
.
.
m1  m 3  m
assume
.
.
m T03
P03
Me 423 Spring 2006
=
m T01
P01
x
P01
P
T
x 02  03
P02
P03
T01
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
.
m
T01
P01
and
P02
P01
are fixed by the chosen OP on the C¢
P03
P02
is assumed to be constant.
Neglecting inlet and exhaust pressure losses Pa = P01 = P04
.
m T03
is a function of
P03
Me 423 Spring 2006
P03
P04
P03
P03 P02
=
.
P04
P02 P01
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
Now in the flow compatibility the only unknown is T03 / T01
The rest can be obtained from C¢ and T¢.
Thus,
.
m T03
P03
P
P
T 03
=( .
) . 02 . 03
T 01
P01 P02
m T01
P01
Thus, knowing T01, T03 can be calculated.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
• Having determined T03 , the SPEED COMPATIBILITY :
N
=
T03
by
N
T03
N
x
T01
T01
T03
and
and
P03
P04
with T ¢

t
• The compressor & turbine temperature changes can be
determined.
T012
T034
Me 423 Spring 2006
T01
P02 (  1)/ 

(( )
 1)
c P01
1
 t T03 (1  (
)  1/  )
P03 / P04
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
And the NET POWER corresponding to selected OP is :
.
  m CpG T034 
1
m
.
m Cpa T012
m could be calculated knowing P01 , T01
c) Having matched the C¢ & T¢ it is necessary to ascertain
whether the work output corresponding to the OP is
compatible with that required by the driven load.
For this; variation of power with speed "P(N)" should be
known. This will indicate whether the OP selected
represents a valid solution (Equilibrium).
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
Examples:
• If the engine were run on a test bed, Coupled to an
electric/or hydraulic dynamometer, the load could be set
independent of speed. Then, it is possible to operate at
any point on C¢ within safety limits (T03 , N).
• With a Propeller load - Power absorbed varies with as N3
of propeller. Knowing ṁ and gear ratio, the load
characteristics in terms of Pout turbine vs Nturbine can be
plotted which corresponds to a single Poutput per constant
speed curve N / T01
i.e single point on a fixed C¢.
• Only at this point the required output is given.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
FIG.3 Load Characteristics
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
• Then the single point on each constant speed line of the
C¢ has to be found.
• This is done by trial error, taking several OP on the C¢
and establishing the power output for each OP.
• If the power output by turbine is not equal to power
required by propeller then the engine will not be in
equilibrium but accelerate or decelerate.
• Finding the equilibrium points on a series of constant
speed lines, and joining them the equilibrium running line
is obtained.
• The most common type of load used with a single shaft
GT is the ELECTRIC GENERATOR which runs at
constant N with the electrical load varying .
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
• Then the single point on each constant speed line of the
C¢ has to be found.
• This is done by trial error, taking several OP on the C¢
and establishing the power output for each OP.
• If the power output by turbine is not equal to power
required by propeller then the engine will not be in
equilibrium but accelerate or decelerate.
• Finding the equilibrium points on a series of constant
speed lines, and joining them the equilibrium running line
is obtained.
• The most common type of load used with a single shaft
GT is the ELECTRIC GENERATOR which runs at
constant N with the electrical load varying .
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
FIG.4 Equiblirium Running Lines
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
• The equilibrium running line for a generator set would
correspond to a particular line of constant N / T01
• Each point on the line would represent a different value of
T03 and Pout.
• At each speed it is possible to find by trial error the
compressor OP corresponding to zero net output and
connecting the No-Load Running Line for a Generator
Set is obtained.
• Looking at the C¢ and propeller equilibrium line, the
operation is generally at a high ηc.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Procedure of Obtaining an Equilibrium Running Point
• Generator load results in a rapid drop in ηc as the load is
reduced.
• The location of equilibrium running line w.r.t. surge line
indicates whether it could be brought to full power without
any complications.
• If ERL and SL intersects a blow-off valve around the
compressor rear is employed. No such problem for
bringing up an electric generator (No load condition).
• With the above findings T032 and hence from Combustion
curves, f could be determined for an assumed b
 then, sfc can be calculated.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on single shaft gas turbine
•
The following data refer to a SSGT operating at design speed:
Ambient conditions:Pa=1.013 bar, Ta=288 K, m=98%
(Neglect all pressure losses!)
Calculate: T03 for Power=3800 kW
1) Establish the T03 for each point given on the CC
2) Establish (T02 - T01), (T03 - T04) and find Pout
3) Plot T03 vs Pout to find the T03 for Pout =3800 kW
•
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on single shaft gas turbine
 .
T03  m T03

T01  P03

1)

m T01   P02 P03 
T
139  5
     03 
 2.11
P01   P01 P02 
T01
329

.
/
1 

T034  0.87  1285 1  1/ 4   370K
 5 
288
(5)1/ 3.5  1  200.5K
0.84
T012 
 T03  1285K
.
.
m
m T01
P01

.
Pa
 19.6kg / s
Ta
  m Cp G  T034 
Me 423 Spring 2006
1
m
.
(m Cp a  T012 )  4305kW
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Equilibrium Running of a Gas Generator
• The GG performs the same function for both the jet engine and
free turbine engine.
• It generates continuous flow of gas at high pressure and
temperature, to be expanded to lower pressure to produce either
shaft work or a high velocity propulsive jet.
• The compatibility of speed and flow are the same as the single
shaft engine.
Thus;
T
N
N
T03
=
T01
.
01
T03
.
m T03
P03
Me 423 Spring 2006
x
=
m T01
P01
*
P01
P
* 02
P02
P03
T03
T01
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Equilibrium Running of a Gas Generator
• However, the pressure ratio of the turbine is not known.
• It must be determined by equating the turbine work to the
compressor work.
• The work requirement;
m Cpg  T034 = Cpa  T012
 T034
 T012
T01
Cpa
1
or
=
*
*
.
T03
T01
T03
Cpg m
• These equations are linked by (T03/T01) and a trial-anderror procedure is necessary to determine T03 for any
arbitrary point on C¢
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Equilibrium Running of a Gas Generator
.
a) Select a comp. OP
b) Calculate
N / T01
P02 m T01
,
,
, c
P01
P01
 1
T01 P02  1
(( )
)
 T012
from  T012 =
T01
c
P01
.
c) Guess a value of P03/P01 & calculate
m T03
P03
from T¢
d) Find T03 / T01 from FLOW compatibility
e) Using T03 / T01
COMPATIBILITY
Me 423 Spring 2006
calculate
N / T03
from SPEED
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Equilibrium Running of a Gas Generator
f) With
N / T03
g)Calculate
and P03 / P04 find c from T¢
 T034
(
) from
T03
 T034
1
= t (1- (
)  1/  )
T03
P03 / P04
h) Calculate (T03/T01 ) using (T034/T03) and POWER
COMPATIBILITY
i) Check T03/T01 with the "one" from flow compatibility (Step d)
j) If different modify P03/P04 and repeat the steps c to i until
obtaining the correct T03/T01
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Equilibrium Running of a Gas Generator
k) The agreement of T03/T01 indicates that the turbine OP is
compatible with the compressor OP for the temperature
increase in CC satisfying T03/T01.
It is not necessary to calculate this for a series of points
because the downstream components impose limits on
the operating zone of the C¢.
This could be repeated for a series of points and points of
constant T03/T01 could be joined up, but unnecessary
since the flow compatibility with the downstream
components (power turbine/or/ propelling nozzle restricts
the operating zone on the C¢.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Equilibrium Running of a Gas Generator
• The matching procedure outlined here has been
developed on the assumption that turbine ¢ do not exhibit
a variation of m T03 / P03 with
N / T03
This is true if the flow correspond to choked mass flows.
•
If not choked; before guessing P03 / P04
*Guess T03/T01 calculate N / T03 from speed compatibility
*calculate
m T03 / P03
from flow compatibility
*Then P03 / P04 and ηt can be obtained from T¢
*T034/T03 can be calculated
compatibility T03/T01
and
the
GG
work
*Compare T03/T01 with the initial guess.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
The matching is done by select a point on C¢.
i) Flow compatibility i.e mass flow of GG = mass flow FT
.
.
m T04
m T03
P03
=
x
*
P04
P03
P04
T04
=
T03
1 -  T034
and
T03
T04
T03
 T034
1
= t (1- (
)  1/  )
T03
P03 / P04
where
ii) The pressure ratio available is fixed by the compressor
and GGT press ratios.
P04
P02
P03
P04
=
x
x
Pa
P01
P02
P03
Inlet and exit duct losses ignored.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
iii) Having found the pressure ratio across the power
Turbine, the value of
m T04 / P04 can be found from the
FT¢.
iv) If m T04 / P04 from (i) and (iii) do not match; a new
point on the constant speed C¢ has to be selected and
this procedure has to be repeated until the flow
compatibility between 2 turbines is satisfied.
• For each N / T01 line on the C¢ there will be only one
point which will satisfy both the requirement of the GG
and the flow compatibility of the FT.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
• Equilibrium running line can be produced for different
N / T01 on C¢. The running line for the FT engine is
independent of the load and determined by the
swallowing capacity (ṁ) of the PT.
• FT engine has quite a different load performance than the
single shaft GT.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
FIG.5 Equilirium Running Line for Free Turbine
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Matching of 2 TURBINES IN SERIES
• The iterative procedure of a FT/GG matching can be
simplified if the 2-Turbines in series are considered.
• The variation of t at any pressure ratio is not large,
particularly in the restricted range of operation. As a
result the change in t does not affect T03 / T04 so has a
little effect on m T04 / P04
• Therefore, a mean value of ηt is taken at any given
pressure
ratio. Then,.
.
m T04 / P04  f (m T03 / P03 , P03 / P04 , t )
Now the GG turbine exit conditions can be mapped on
the GGT¢.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
FIG.6 Operation of Turbines in Series
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
• The flow compatibility between the 2 turbines places a
major restriction on the OP of GGT.
• As long as the PT is choked, the GGT will operate at a
fixed ND point at all choked OP.
• With the PT unchoked the GG will operate at a fixed
pressure ratio for each PT pressure ratio (i.e. fixed OP)
• Thus the maximum pressure ratio across the GGT is
controlled by choking PT. (i.e the SWALLOWING
capacity the GT).
• The turbine pressure ratios can be expressed in terms of
the Rc as:
P03
P03
P02
Pa
=
.
x
P04
P02
P01
P04
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off-design Operation of Free Turbine Engine
FIG. 7 Compressor Pressure Ratio vs GGT Pressure Ratio
• For any value of the compressor pressure ratio, GGT
pressure ratio can be obtained. Thus m T03 / P03
and
T034 /T03 are fixed for GG flow compatibility & GG power
compatibility. Thus for the GG, pressure ratio iteration is not
necessary to find the correct equilibrium point.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation of Power Output & Sfc with Output Speed
of a Free Turbine Engine
• Power output of a FT engine = ṁ Cpg  T045
where
 T045 = tp T04 (1  (
1
)
P04 / Pa
 1

)
FIG.8 Variation of Power Output with Output Speed
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation Of Power Output & sfc with Output Speed
of a Free Turbine Engine
• power output for each equilibrium running point (one for
each compressor speed);
i)
P04 /Pa will be known
ii) T04 can be calculated from
T04 = T03 - T034
knowing Pa, Ta ; m can be found from
m T01 / P01
P04
N PT
tp from PT ¢ but tp = f (
,
)
Pa
T04
• Free turbines are used to drive a variety of loads each of
which are different (pump, propeller, electric generator),
each with different vs Npt ¢ .These curves are quite flat in
the higher Npt region where pt is fairly constant.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation Of Power Output & sfc with Output Speed of a Free
Turbine Engine
FIG.9
Variation of sfc
With Power Output
• sfc increases as power is reduced, since as fuel flow
decreases; Nc decreases, T03 decreases; but as T03
decreases cycle decreases.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation of Power Output & sfc with Output Speed of
a Free Turbine Engine
• Fuel consumption can be calculated similar to the single
shaft units since the fuel consumption depends only on
GG parameters. There will be one value for each
N1 /
as Pout
T01 . sfc however, is a function of both Nc and Npt
• The off-design performance can be expressed by plotting
sfc vs Pout for different Npt. This shows the performance of
the unit when coupled to different types of loads.
•
Although for convenience Ncomp is chosen as the
independent variable; in practice the fuel flow is the
independent variable. A chosen value of fuel flow and
(T03) determines Ncomp and therefore Pout.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Torque Characteristics
• In case of a GT delivering shaft power, the variation of
torque with output speed at a given power determines its
suitability for different applications (e.g. high starting torque
for traction).
a) For the single shaft engine the compressor is
constrained to turn at some multiple of load speed.
Load speed decrease = Compressor speed decrease
unsuitable for traction (since m decrease out decrease)
b) Normal curve of Internal Combustion Engine is flat.
c) Free power turbine has a favourable torque ¢ over a
wide load-speed range for a fixed Nc. This is because the
compressor can supply an essentially constant flow at a
given compressor speed irrespective of the FT speed.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Torque Characteristics
• Therefore,
at constant Pout as Npt decrease  t increase.
• The torque might stall at high t or very low Npt.
With a reduction in Npt quite a large increase in
obtained efficiently.
t can be
• But at least a speed gear box have to be used for traction
(usually 5-6 speed automatic transmission is used in
heavy load vehicles)
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Torque Characteristics
FIG.10 Torque Characteristics
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
Given:
m  30kg / s
Rc  6
T03  1200 K
t  0.87
m  0.99
Pa  1.01bar
Calculate:
c  0.84
P032  0.2bar
Ta  288K
.
.
m T03 m T04
,
• Power developed and the turbine ND flows
P03
P04
• If the engine is running at same mechanical speed at
ambient temp. of 268 K, calculate T03, P03 / P04 and Pout
assuming the following:
a)Combustion pressure loss remains constant.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on Gas Turbine with Free Power Turbine
.
.
b)Both turbines are choking with values of m T03 and m T04 as
P04
P03
calculated above. No change in  t
c)At 268 K and the same N, the N / T01 line on the C¢ is a
vertical line with ND flow 5% greater than the design value.
d)Variation of compressor efficiency with pressure ratio at the
relevant value of N / T
is:
01
P02 / P01
c
Me 423 Spring 2006
6.0
6.2
6.4
6.6
0.873
0.843
0.845
0.840
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
Solution:
• Design Point Calculation:
.
OP on CC: m T01
P01
T 03 1200

T 01 288
.
30 288

 504.1
1.01
P02
 6.0
P01
P03
P02  P03
0.2
 1
 1
 0.967
P02
P02
6 1.01
.
m T03 m T01 P01 P02 T03
1
1200

  
 504.1 1.034 
 177.3
P03
P01 P02 P03 T01
6
288
T012
(  1)
 288
T01  P02 
(6)1/ 3.5  1  229.2 K

 1 
( )
c  P01
 0.84
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on Gas Turbine with Free Power Turbine
GG
T034  T012
P04  1 T034 
 1 

P03   t T03 
Cpa 1
1005 1

=229.2 
 =202.9
CpG m
1147 99
 1/ 
4
1 203 

= 1 
 0.42

 0.87 1200 
P03  P02  0.2  6 1.01  0.2  5.86bar
T 04  1200  203  997 K
Power Turbine:
P04 P04 P02 P03 P04




 6  0.967  0.42  2.445
P05 Pa
Pa P02 P03
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on Gas Turbine with Free Power Turbine
P04  2.445 1.01  2.47bar

T045
1
1 1/ 4 

 1/  
 t 1  (
)

0.87

1

(
)   0.174


T04
P04 / P05
2.445 



T045  0.174  997  173.7 K
.
out  m  CpG  T045 m  30 1.147 173.7  0.99  5918kW
.
m T03
P03
.
 177.3
Me 423 Spring 2006
m T04
P04

30 997
 383.5
2.47
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
OFF DESIGN
At Ta= T01 =268K
.
m T01
P01
 1.05  504.1  529.5
T01
T01
 0.931 
 0.965
288
288
• If the PT remains choked, the GGT will be constrained
to operate at a fixed ND point and thus the value of
T034
 203/1200  0.169 as for the design condition
T03
The Work Compatibility:

T012 T034
T03  Cpg
T03
T03
1147



m  =0.169 
 0.99 
=0.191
T01
T03
T01  Cpa
1005
T01
T01

Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
hence
T03
T012
=5.23
A
T01
T01
Flow Compatibility
.
.
m T03
m T01 P01
T03




P03
P01
P03
T01
T03
P
 0.335  03  B
T01
P01
Now the problem is to find the OP that satisfies A and
B simultaneously for T03 / T01
With the variation in efficiency;
 .
m T03

c  f
 P03

Me 423 Spring 2006




Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
(  1)

T012
1  P02 


 1
( )
T01
c  P01

P02 P01

With the constant value of CC loss P03 
P01 P02 /P03
Iterations Tabulated :
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
(  1)

T012
1  P02 


)
 1
(
T01
c  P01

With the constant value of CC loss
P03 
P02 P01

P01 P02 /P03
Iterations Tabulated:
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
• Solving Graphically the required pressure ratio :
P02 / P01 = 6.41
with T03 / T01 = 4.34
• Therefore; To3 = 4.34*268=1163K
• P developed can be calculated;
• since the GGT still operates at the same ND point
T034
 0.169
T03
P03
 2.373
P04
T034  1163  0.169  197.2K

T045
1
1 1/ 4 

 1/  
 t 1  (
)
)   0.174
  0.87  1  (
T04
P04 / P05
2.445 



.
m T01
P01
.
 529.5  m 
Me 423 Spring 2006
529.5 1.01
 32.7kg / s
268
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Example on gas turbine with Free Power Turbine
• Power output
P = 32.7kg/s* 1.147J/kg.K*179,6K*0,99= 6680kW
• Thus on a cold day a decrease of Tamb to To1=268K
results in a decrease of max. cycle temperature from
1200K to 1163K.
• T03/T01 increases from 4.17 to 4.34 due to the increased
N / T01
• Power increases from 5910 to 6680 kW. This is due to
increase of mass flow rate and compressor pressure
ratio.
• The beneficial effect of low Ta on GT is evident also the
adverse effect of increase of Ta.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Off Design Operation Of The Jet Engine
Propelling Nozzle Characteristics
•The propelling nozzle area is determined from the design
point calculations.
•A fixed nozzle area has a major influence on the
off-design operation.
•The nozzle ¢ in terms of ND variables is given in terms
of m T04 / P04 and P04/Pa
.
m T04
T04
V5 A5 P5 T04
= V5 A5 5
=
.
.
.
P04
P04
T04 R P04 T5
V52
1
= 2 Cp  j (1- (
)  1/  )
T04
P04 / P5
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Propelling Nozzle Characteristics
T5
T T
1
= 1 - 04 5 = 1 -  j (1- (
) 1/  )
T04
T04
P04 / P5
• For a nozzle of given area and j
.
m T04 / P04 = f (P04 / P5 )
• These are valid up to the critical point.
The CRITICAL point of the nozzle is when
P04
1  - 1  /(  1)
= 1 / (1(
))
Pc
j  + 1
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Propelling Nozzle Characteristics
FIG.11 Propelling Nozzle Characteristics
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Propelling Nozzle Characteristics
• for P04/Pa > P04/Pc , the nozzle is choked P5 = Pc > Pa and
m T04 / P04 = const (not a function of P04/Pa ).
• The similarity between this and the turbine ¢ is evident.
• When the nozzle is choked
Tc
2
=
; V5 = a5 =
T04
 +1
 RT5
i.e (M5  1)
• Generally
V
=
T0
M R
V52
V52
2 R
for choked nozzle
=
=
 -1 2
T04
T05
 +1
1+
M
2
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Matching of GG with Nozzle
• The Nozzle will exert the same restriction on the
operation of the GG as the FT, at STATIC conditions,
• The equilibrium running line can be determined as for FT.
Here the effect of forward speed (Va) on the equilibrium
running line has to be considered.
FORWARD SPEED 
RAM PRESSURE RATIO = f(Ma, ηi)
RAM  P02 increase P04 increase  P04/P5 increase
when choked m T04 / P04 maximum and independent of
P04/P45 thus Va .
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Matching of GG with Nozzle
• Then the Turbine OP will be unchanged because of the
compatibility of flow between turbine & nozzle.
• That is; As long as the nozzle is choked, the equilibrium
running line is uniquely determined by the fixed Turbine
OP and independent of flight speed.
• Practically ALL JET ENGINES during take off, climb and
cruise operate with Choked Nozzle.
• The nozzle may be unchoked when preparing to land or
taxying.
• Since the running line is close to surge line at low
,the effect of Va on ERL has to be
N / T01
considered.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Matching of GG with Nozzle
• Nozzle pressure ratio and Ram pressure ratio can be
related as:
P04
P04
P03 P02
P01
=
*
*
Pa
P03
P02 P01
Pa
• The ram pressure ratio is:
P01
 - 1 2  /  1
= (1 + i (
) Ma )
Pa
2
• Therefore, for a given intake efficiency i ;
P04/Pa = f (GG parameters and flight Mach Number).
• *The same procedure as for the FPT can be followed to
obtain the equilibrium running point.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Matching of GG with Nozzle
FIG. 12 Jet Engine Running Lines
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Matching of GG with Nozzle
• For each compressor speed N / T01 the calculation is
repeated for several Ma to cover the desired range of
flight speed.
• The result  A fan of Equilibrium RL of constant Ma.
• These merge to a single RL at higher N /
the nozzle is choked.
T01 , where
• Increasing Ma pushes the equilibrium RL away from SL at
low compressor speeds.
• Therefore, the Ram pressure rise allows the Rc decrease
for the required flow.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation of Thrust With Rotational-speed;
Forward-speed; Altitude
• The Net Thrust of the jet is;
F = m (V5-Va) + (P5-Pa) A5
• Fnet over the complete range of inlet conditions
(Va, N /
T01 ) is determined by ND quantities as:
.
m T01 P01
F
V5 T04 T03
=
.
(
.

Pa
P01
Pa
T04 T03 T01
• Since: Va =
T01
Me 423 Spring 2006
Va
=
T0a
Va
P5
) + (
-1) A5
T01
Pa
M a R
 1 2
1
Ma
2
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation of Thrust With Rotational-speed;
Forward-speed; Altitude
• When the Nozzle is UNCHOKED;
1
= 2 Cp  j (1- (
)  1/  )
P04 / P5
V5 / T04
• with P5 = Pa and the pressure thrust is 0 since P5 / Pa = 1
• When the Nozzle is CHOKED; V / T = ( 2 R )
5
04
 +1
P5
P04
Pc P04
and P5
Pa
=
P04
.
P02
=
P04
.
Pa
where the critical pressureratio, Pc / P04:
1  - 1  /  1
Pc / P04 = (1 (
))
j  + 1
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation of Thrust With Rotational-speed;
Forward-speed; Altitude
FIG.13 Variation of Thrust (F/ Pa ) with engine speed
(N/T01) and flight speed (Ma)
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation of Thrust With Rotational-speed;
Forward-speed; Altitude
• There;
N
=
Ta
N
.
T01
T01
T01
 -1 2
and
= ( 1+
Ma )
Ta
Ta
2
• The thrust for a given N/T01= f (Ma) ;
although for choked flow there is a UNIQUE ERL.
• Increasing flight speed Va, m*Va= momentum drag
increases P02 increases (i.e RAM increases )
• At low N/T01, momentum drag increase predominates
thus Ma increases  Fn decreases .
• At high N/T01, Ram pressure rise predominates Thus Ma
increases  Fn increases
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
ENGINE SPEED
• Although performance is expressed in terms of ND
speed, N/T01 , the actual mechanical speed N imposes
a limit due to turbine stresses, and controlled.
• If the speed is kept well below this limit, the take-off
thrust is substantially reduced.
• If N exceeds the correct limit:
i) The centrifugal stresses increase with the square
of speed N2
ii) A rapid increase in Turbine Inlet Temperature T03
(2% in N may cause 50K in T03)
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
ENGINE SPEED
• Since the blade life is determined by CREEP, the time
which the high speeds are permitted must be controlled.
Take-off rating t < 5 min 100% Nmax
Climb rating - reduction in fuel flow t < 30 min
at 98 % Nmax
Cruise rating - further reduction in fuel and
rotor speed at 95 % Nmax
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Effect of Ambient Conditions on the take
off rating
Ta:
With Engine running at max speed, Ta  ,N/  Ta 
hence N/T01  ,
along
the equilibrium running line ;
.
m T01
P
decrease 02 decrease
P01
Pa
• Therefore, Ta  
Fn  ( loss of thrust)
T03  T03 = ( T03 / T01 )*T01
• On a hot day T03 > T03max  N  is required, thus Fn 
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Effect of Ambient Conditions on the take
off rating
Pa:
Fn and Pa in direct proportion (since (F / Pa) ...)
Altitude  , Pa  and Ta  ( up to 11000 m)
since as Pa  Fn 
but as
Ta   Fn 
Then Fn 
• Therefore ; thrust decreases with increase in altitude.
• Airports at high altitudes, especially around tropical
zones are critical (Mexico-City, Nairobi ) suffer from this
problem.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation in fuel consumption & sfc with
rotational Speed, forward speed & altitude
• Fuel consumption and fuel capacity of the aircraft
determine the range
• sfc(fuel flow /per unit thrust) indicates economy
Both are functions of N/T01 and Ma.
• With combustion efficiency b assumed,
fuel consumption can be determined from :
m, f/a curves, with ΔT032 .
Therefore; fuel flow = f ( N/Ta ,Ma, Pa, Ta)
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation in fuel consumption & sfc with
rotational Speed, forward speed & altitude
• Dependence of fuel flow on Ambient conditions can be
eliminated by ND fuel flow m f
Pa T a
• The fuel parameter slightly depends on Ma when based
on T01 and P01. They merge to a single line, for the
choked nozzle conditions.
sfc  with ( altitude  ) since Ta 
but since sfc  f(Pa)
this is not as marked Fn .
* sfc  with Ma .
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Variation in fuel consumption & sfc with
rotational Speed, forward speed & altitude
FIG. 14 S.f.c. Curves
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Methods of Displacing the Equilibrium
Running Line
• If the Equilibrium Running Line (ERL) intersects the Surge
Line (SL), it is not possible to bring the engine up to full
power directly.
• The compressor may surge when the engine accelerates
even ERL is not cutting the SL.
• Many high performance compressors have a kink in the
SL.
• A running line intersecting SL at low N/T01 and at the kink
is shown in Figure 15.
To overcome ERL is lowered down in dangerous regions.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Methods of Displacing the equilibrium
running line
• BLOW-OFF is a method to achieve this.
• Air is bled from some intermediate compressor stage.
 Some turbine work is wasted.
blow-off valve only operates when it is essential.
• Variable Area Propelling Nozzle; an alternative method
to blow-off.
• Either method will produce a reduction in P02/P01 at a
given N/T01, hence lower the ERL.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Methods of Displacing the equilibrium
running line
FIG. 15 Effect of Blow-off and Increased Nozzle Area
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Methods of Displacing the equilibrium
running line
FIG. 16 Effect of Variable Area Propelling Nozzle
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP
Prediction of Performance for GT
Methods of Displacing the equilibrium
running line
• In a variable area nozzle as nozzle area increases, A5
increases (P03/P04 ↑ ,so ΔP034/T03 ↑).
If N/T01 is held constant P02/P01 ↓.
Therefore, RL will be moved away from SL. To keep
N/T01 constant fuel flow to be reduced.
P02
T03

P01
T01
T03
1

T01
 T034 / T03
P02
1

P01
 T034 / T03
• for N/T01 held constant and A5↑ ;
P03
 T034
P02
as
increase
increase 
decrease
P04
T03
P01
ERL will be removed away from SL.
Me 423 Spring 2006
Prof. Dr. O. Cahit ERALP

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