Prerequisite - Thermodynamics/ Propulsion Review of Fundamentals/ Ideal Turbojet Performance

1. Aeropropulsion
Unit
Component Performance
2005 - 2010
International School of Engineering, Chulalongkorn University
Regular Program and International Double Degree Program, Kasetsart University
Assist. Prof. Anurak Atthasit, Ph.D.

2. Aeropropulsion
Unit
Kasetsart University
2
A. ATTHASIT
Introduction
•Back to the real world
–The working fluid behaved as a perfect gas with non-constant specific heats.
–The engine components will be characterized by figures of merit that model the component’s performance of real air-breathing engines.
Variation in gas properties
Component performance
Inlet diffuser, Exhaust nozzle
Wall-boundary viscous
Fan, Compressor, Turbine
Viscous inter-blade
.. Separation, mixing
Combustion Chamber
Enthalpy Jump

3. Aeropropulsion
Unit
Kasetsart University
3
A. ATTHASIT
Objective of Study
1.Variation in Gas Properties
2.Component Performance
1.Inlet and diffuser performance
2.Compressor and turbine efficiency
3.Burner efficiency
3.Summary: Component figures of merit

4. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 4
Variation in Gas Properties
Specific heats at constant pressure and volume:
p
v
dh C dT
de C dT


In general
( )
( )
p p
v v
C C T
C C T


There is often a simplifying assumption of constant specific heats, which
is a valid approximation to gas behavior in a narrow temperature range
p p
v v
C Const
C Const


1
1
, ,
1 1
p v
p v
p v
p v
v v
C C R
C C
R R
C C R
C R C R
C C


 
 
 

   
 
0
0
1500
? hot  
? cold  
1 1
1
1
t t u
pt t
t t
pt t c
pc t c
R
C R
M
C
C
 
 
 
 
 
 




5. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 5
Inlet and Diffuser Pressure Recovery
0 1 2 3 4 5 9
0 m
f m
0
f
m
m
0 P
1 P
0 t P
t0 T
2
0
2 p
V
C Air is retarded by the variation
of air tube before entering an
inlet Resulting by increasing
the static pressure
t0 T
2 t P
0 s 2 s
2 P
Adiabatic  Tt0=Tt1=Tt2
t 2s T
Pressure drop due to viscous flow effect
Isentropic efficiency of the diffuser:
2
2 0 2 0 0
0 0 0 0 0
0
0 2 1
0 0
0
0
1
1
1
1 1
1 1
1
t s
t s t s
d
t t t
t t s
t r d r d
d
t r r
T
h h T T T
h h T T T
T
T T
T T
T
T



   

 


 
  
 


 
  
 


6. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 6
Compressor Efficiency
0 1 2 3 4 5 9
0 m
f m
0
f
m
m
2 t P
3 t P
t3i T
2 s 3 s
Adding more work to
compete the loss
t3 T
Ideal Actual
t 2 T
3 2
3 2
3 2
3 2
ideal work of compression for given
actual work of compression for given
1
1
Here is the ideal compressor temperature ratio (isentropic)
c t i t
c
c t t
t i t ci
c
t t c
h h
h h
T T
T T







 

 
 
 
Isentropic efficiency of the compressor:
1
1
1
c
c
c

 







7. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 7
Compressor Efficiency
0 1 2 3 4 5 9
0 m
f m
0
f
m
m
2 t P
3 t P
t3i T
2 s 3 s
t3 T
Ideal
t 2 T
ideal work of compression for a differential pressure change
actual work of compression for a differential pressure change c e 
Polytropic efficiency of the compressor:
Actual
ds
1
2 2 2
1 1 1
1
1
1/
1/
1 1
1
where
1 1
P
p
C
R
ti ti
ti ti
t t t
t
t t
ti t ti t
t t t t
dT dP
C R
T P
P T T
P T T
T const P
dT dP
const const
dP dP P
T
const
P P
dT T dT dP
dP P T P










 
 



 
   
      
   
  

     
 
 
   
From Gibbs Equation, the
isentropic relationship
gives:
3 3
2 2
1
/
/
1 / 1
/
1
ln ln
c
i ti ti ti t
c
t t t t
t t t t
c
t t t c t
t t
t c t
e
c c
dw dh dT dT T
e
dw dh dT dT T
dP P dT dP
e
dT T T e P
T P
T e P


 
 


 

   
 
  

 
 
ec is constant
for a
differential
pressure
change

8. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 8
Compressor Efficiencies
In-class Practice:
Prove
• Obj: Able to
use the
fundamental
equation
under the
correct
assumptions
Analysis
• Obj:
Understand
the physical
meaning of
each
parameters
Calculation
• Obj: Able to
solve the
relations
under the
constraints of
corrected unit,
constant, …
etc.
We plan to construct a 16-stage compressor given
c=25. Each stage has stage=0.93. Find
1. Pressure ratio for each stage
2. Polytropic efficiency ec
3. Prove that the compressor efficiency can be
written in
4. Compressor efficiency
1
1
1
1 (1/ ) 1 1
c
c N
s s






 




  
     
     
1. 1.223
2. 0.9320
3. -
4. 0.8965

9. Aeropropulsion
Unit
Kasetsart University
9
A. ATTHASIT
Take a Break!
The Next-Generation Single- Aisle (NGSA) aircraft, Pratt & Whitney is backing the concept of a geared fan in which the fan is connected to the rest of the low-pressure system by the use of a reduction gear. Through the interposition of gearing each component can work at its own optimal speed, resulting in greater efficiency. The thrust bracket of interest here is the range 90kN to 160kN, the main focus being on aircraft with around 150 seats.
Decoupling by means of gearing enables the fan to rotate at only one third of the speed of the rest of the low-pressure system. This means we can raise the speed of the low-pressure compressor and turbine. It allows us to have just three stages in the low-pressure compressor instead of six for a given thrust.
High BPR 11:1
Reduction in:
•Fuel Consumption
•Maintenance Cost
•Noise Emission

10. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 10
Turbine Efficiency
In-class Practice:
5 t P
t 4 T
4 s
Ideal
t5i T
Ideal
Prove
• Obj: Able to
use the
fundamental
equation
under the
correct
assumptions
Analysis
• Obj:
Understand
the physical
meaning of
each
parameters
Calculation
• Obj: Able to
solve the
relations
under the
constraints of
corrected unit,
constant, …
etc.
1. Complete the T-s diagram of turbine indicated below
2. Show that the isentropic efficiency of turbine is
3. Prove that the turbine stage efficiency is related to
turbine efficiency as
4. Show that the turbine polytropic efficiency is given
by
1
1
1
t
t
t









1
1
1 1 (1/ ) 1
1
N
s s
t
t




 




  
     
      

 1 t e
t t

    

11. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 11
Burner Efficiency and Pressure
Loss
Two efforts, we
are concerned
about the burner 1. Incomplete
combustion of the
fuel
2. Total Pressure loss
C m
f m
C f m m 4 3
4 4 3 3
4 3
( )
( )
( )
a f t a t
b
f PR
a f p t a p t
b
f PR
a f pt t a pc t
b
f PR
m m h m h
m h
m m C T m C T
m h
m m C T m C T
m h



 

 

 

Combustion Efficiency
4
3
1 t
b
t
P
P
  
Total Pressure Loss in Combustor
Actual
Ideal

12. Aeropropulsion
Unit
Kasetsart University
12
A. ATTHASIT
Exhaust Nozzle Loss
The primary loss due to the nozzle has to do with the over- or under expansion of the nozzle. Note that we still have adiabatic assumption for flow in nozzle.
909511tntnPPPP     

13. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 13
Component Figures of Merit for
Different Technological Levels
0 1 2 3 4 5 9
0 m
f m
0
f
m
m
1. This table lists typical
values for the figures of
merit that correspond to
different periods in the
evolution of engine
technology.
2. The values have
changed as technology
has improved over the
years.

14. Aeropropulsion
Unit Kasetsart University A. ATTHASIT 14
Conclusion
*
2
1
*
2
1
1
*
*
2
*
1
2( 1)
2
*
1
2
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1 2
1
2
T
T
M
P
P
M
P
P
T
M
T
P
m AV AM
R T
M
A
A M











 










  
 
 
  
 
  
           
  
 
   
           
 
    
    
    
  
 
 
2
0
0 t
dA d du
A u
udu dP
dh dh udu
dP d dT
P T
a
P







  
 
  
 

P dP
T dT
d
A dA
u du
 





P
T
A
u

dx
2
dP
P 
See You
Next Class!