Aircraft propulsion turbomachine 2 d
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Transcript of Aircraft propulsion turbomachine 2 d
Aeropropulsion Unit
Introduction and 2-D Analysis in
Turbomachinery
2005 - 2010 International School of Engineering, Chulalongkorn University Regular Program and International Double Degree Program, Kasetsart University
Assist. Prof. Anurak Atthasit, Ph.D.
Aeropropulsion Unit
2 A. ATTHASIT Kasetsart University
Work input into compressors
Intro : Thermodynamics concept
Compressor Work/Mass
compressor p3 t3 p2 t2w C T C T
compressor t3 t2w h h
Compressor Pressure Ratio
1t3 t3
c
t 2 t 2
P T
P T
1
p t2
compressor c
c
C Tw 1
Compressor Efficiency
Aeropropulsion Unit
3 A. ATTHASIT Kasetsart University
General Design Consideration
Intro : Comp. Design
First step of design : Choice of stage loading
(ex. the pressure rise in relation to the
number of stages and the rotational speed)
Decision to have an axial radial compressor
(ex. For aircraft propulsion the high flow rate per
unit area of the axial is a big advantage)
(ex. Radial compressor has a huge cost advantage
over the axial)
Aeropropulsion Unit
4 A. ATTHASIT Kasetsart University
Axial Compressor
Preliminary design : at a mean radius (pitchline)
Criteria have to be chosen for satisfactory
• Blade loading
• Pressure rise at the walls
• Maximum Mach number
Aeropropulsion Unit
5 A. ATTHASIT Kasetsart University
Blade Loading : de Haller n° Criteria for endwall loading or pressure rise :
De Haller number 2 1V / V 0.72
De Haller (1953)
But lowing value ---> excessive losses
Aeropropulsion Unit
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Blade Loading : diffusion factor
Diffusion factor
High fluid deflection = high rate of diffusion
Definition & termology :
Aeropropulsion Unit
7 A. ATTHASIT Kasetsart University
Blade Loading : diffusion factor
Diffusion factor
High velocity gradient ---> high boundary layer thicnkness ---> high losses
w1 2
max 2
1 1
C sV V
V V 2 cDV V
w2
1 1
CV sD 1
V 2V c
max 1 w
sV V 0.5( C )
c When
csolidity
s
Aeropropulsion Unit
8 A. ATTHASIT Kasetsart University
Diffusion factor
Diffusion factor
w2
1 1
CV sD 1
V 2V c
Wide range of cascade NACA tests
Criterian's limit :
D < 0.6
Advantage :
'D' help to construct
the velocity diagram
Aeropropulsion Unit
9 A. ATTHASIT Kasetsart University
Many criterias left for prelim-design
Degree of reaction
Degree of reaction (°Rc) : T1
T2
T3
2 1 2 1c
3 1 3 1
h h T TR
h h T T
One
stag
e of
com
pre
ssor
°Rc desirable is 0.5 (share the burden)
Stage loading
p tt t
2 2 2
c Th h
( r ) U U
0.3 0.35
Aeropropulsion Unit
10 A. ATTHASIT Kasetsart University
Many criterias left for preliminary design
Flow Coefficient
a1 a1C C
r U
0.45 0.55
Flow coefficient
Aeropropulsion Unit
11 A. ATTHASIT Kasetsart University
3D Flow Field
Typical gas turbine design procedure
Design procedure
Market
research
Specification Customer
requirements
Preliminary studies: Choice of cycle,
Type of turbomachinery, layout
Turmodynamic design point studies
Aerodynamics of compressor,
turbine, Intake, exhaust, etc.
Ex: Take-off-Thrust
(12,000 N)
c 4.15 m 20kg / s
4T 1100K
Axial flow, Turbojet
Rotational Speed,
Annulus Dim,
N° of stages,
Air Angles,
Balde Design, Etc.
Aeropropulsion Unit
12 A. ATTHASIT Kasetsart University
3D Flow Field
Typical gas turbine d'sign procedure
Design procedure
Ex: Take-off-Thrust
(12,000 N)
c 4.15 m 20kg / s
4T 1100K
Axial flow, Turbojet
Rotational Speed,
Annulus Dim,
N° of stages,
Air Angles,
Balde Design, Etc.
Desired
Performance
Parameters
Turbomachinery
Design Criterias
Blade Loading,
etc..
Aeropropulsion Unit
13 A. ATTHASIT Kasetsart University
Three Dimensional Flow
Sum of 2-D flow:
- Throughflow field
- Cascade field (blade-to-blade)
- Secondary flow field
3-D Flow
Aeropropulsion Unit
14 A. ATTHASIT Kasetsart University
Throughflow field
2-D Flow
Aeropropulsion Unit
15 A. ATTHASIT Kasetsart University
Throughflow field Mass flow parameter
2-D Flow
Pm PV V PV M
A RT RRT RT T
1
1 2t t 2
t t
T Tm P 1MFP M M 1 M
A P R P R 2T
Mass Flow Parameter (MFP)
Aeropropulsion Unit
16 A. ATTHASIT Kasetsart University
Cascade field
2-D Flow
Aeropropulsion Unit
17 A. ATTHASIT Kasetsart University
Cascade field
2-D Flow
Aeropropulsion Unit
18 A. ATTHASIT Kasetsart University
Secondary field
2-D Flow
Aeropropulsion Unit
19 A. ATTHASIT Kasetsart University
Coordinate systems
2-D Flow
1 2 3
• Absolute coordinate : U,u2,V2
(fixed to the compressor housing)
U( r )
2V
2u2RV
• Relative coordinate : V2R
(fixed to the rotating blades)
Aeropropulsion Unit
20 A. ATTHASIT Kasetsart University
Euler's Equation
Designing Tools
Fluid Mech Eq :
Torque & Work :
A e e i im( r v rv )
C AW
1st Law of Thermo Eq :
C te tiW m( h h )
te ti e e i ih h ( r v rv ) 'This relation will be used to obtain total
temperature changes throughout the blade' p te ti e e i iC (T T ) ( r v rv )
Aeropropulsion Unit
21 A. ATTHASIT Kasetsart University
Velocity Diagrams Velocity Diagrams
Aeropropulsion Unit
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Velocity Diagrams & Euler's Equation Velocity Diagrams
p t2 t1 2 2 1 1C (T T ) ( r v r v )
2r1r
2 1 2
p t2 t1 1 2
1
u uC (T T ) r tan tan
r u
2 1 2
p t2 t1 2 1
1
u uC (T T ) r tan tan
r u
Aeropropulsion Unit
23 A. ATTHASIT Kasetsart University
ii i i i i ii i i i
i i i i i
PPV cos V cos PmV cos M
A RT RRT RT T
Velocity Diagrams & Flow Annulus Area Velocity Diagrams
2r1r
i
ti
i
ti i M
m TA
P cos MFP
Aeropropulsion Unit
24 A. ATTHASIT Kasetsart University
Coordinate systems : important!
2-D Flow : Caution!
1 2 3
• Absolute coordinate : U,u2,V2
(fixed to the compressor housing)
• Relative coordinate : V2R
(fixed to the rotating blades)
t1 t1R t1 t1RT ,T ,P ,P
t 2 t2R t2 t2RT ,T ,P ,P
Aeropropulsion Unit
25 A. ATTHASIT Kasetsart University
Mean radius geometry
Constant mean radius
Nomenclature for constant mean radius
Constant Mean Radius
Aeropropulsion Unit
26 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
rm
t1 t1
m
1 3
t321 3
1 t1
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
PuM M 0.7, 1.1, 1.3
u P
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Stage calculation
t1 t1R t1 t1RT ,T ,P ,P
t 2 t2R t2 t2RT ,T ,P ,P
&Velocity diagram
t1
1 2
1
TT
1 1 / 2 M
t1
1 /( 1 )2
1
PP
1 1 / 2 M
1t1 t1
1 1
P T
P T
Aeropropulsion Unit
27 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
t1 t1
m
1 3
t321 3
1 t1
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
PuM M 0.7, 1.1, 1.3
u P
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Step 1: Find Triangle "V" at Station 1
Properties
Geometry
V_Compo
V_Compo
(relative)
Properties
(relative)
1T 1a1P
1 1 1V M a 1 1 1u V cos 1 1 1v V sin
1
t1
1
t1 1 M
m TA
P cos MFP
U r
1R 1v r v 2 2
1R 1 1RV u v 1R1R
1
VM
a
t1R 1 1RT f (T ,M , ) t1R 1 1 t1RP g( P ,T ,T , )
Aeropropulsion Unit
28 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
t1 t1
m
1 3
t321 3
1 t1
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
PuM M 0.7, 1.1, 1.3
u P
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Step 2: Find "P&T" at Station 2
Properties :
t 2 t2T ,P ?
t 2R t2RT ,P ?
t 2 t3 t1 c,stageP P P ( 1 ) /
t 2t 2 t3 t1
t1
PT T T
P
t 2R t1R t2R t1RT T ,P P
Aeropropulsion Unit
29 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
t1 t1
m
1 3
t321 3
1 t1
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
PuM M 0.7, 1.1, 1.3
u P
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Step 3: Find Triangle "V" at Station 2 ?
Which Eq can link "V" from station 1-2 ?
2 1 2
p t2 t1 1 2
1
u uC (T T ) r tan tan
r u
Euler's Equation :
Then 2 is determined
Aeropropulsion Unit
30 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
t1 t1
m
1 3
t321 3
1 t1
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
PuM M 0.7, 1.1, 1.3
u P
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Step 4: Find Triangle "V" at Station 2
22 1 2R 2 2
1
uu u ,v u tan
u
2RV
1 22 2R 2
2
vv U v , tan
u 2V
Step 5: Find "T&P" at Station 2
/( 1 )2
2 22 t2 2 t2
P t2
V TT T ,P P
2C T
Aeropropulsion Unit
31 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
t1 t1
m
1 3
t321 3
1 t1
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
PuM M 0.7, 1.1, 1.3
u P
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Step 6: Find the rest at Station 2
2 2 2a ,M ,A
Step 7: Find the rest at Station 3
t3 t3R t3 t3RP ,P ,T ,T ?
3 3P ,T
3 3 3 3 3a ,V ,u ,v ,A
Aeropropulsion Unit
32 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow without loss
Rotor : Adiabatic in the relative reference frame
Stator : Adiabatic in the absolute reference frame
§ I M P O R T A N T §
Aeropropulsion Unit
33 A. ATTHASIT Kasetsart University
Flow with loss : Introduction
Flow with loss
Adiabatic Stage Efficiency s
( 1 ) /
t3s t1 t3s t1 t3 t1s
t3 t1 t3 t1 t3 t1
h h T T ( P / P ) 1
h h T T T / T 1
When t t3 t1T T T
/( 1 )
t3 ts
t1 t1
P T1
P T
Aeropropulsion Unit
34 A. ATTHASIT Kasetsart University
Flow with loss : Introduction
Flow with loss
ti ti ti t t tc
t t t t t t
dh dT dT / T dP / P1e
dh dT dT / T dT / T
Adiabatic Polytropic Efficiency ce
t3 t1c
t3 t1
ln( P / P )1e
ln(T / T )
0.9
(Preliminary design)
When t t3 t1T T T
c ce /( 1 ) e /( 1 )
t3 t3 t
t1 t1 t1
P T T1
P T T
Aeropropulsion Unit
35 A. ATTHASIT Kasetsart University
Flow with loss : Life is still not easy …
Flow with loss
Adiabatic Polytropic Efficiency
Adiabatic Stage Efficiency When
are
unknown …
Aeropropulsion Unit
36 A. ATTHASIT Kasetsart University
Flow with loss : Experiment data
Flow with loss
Cascade tests result :
• The optimum angle
(minimum loss)
• Profile drag coefficient
(cascade efficiency)
(must be increased to account
for end losses (e.g., tip leakage,
wall boundary layer or cavity
leakage)
Aeropropulsion Unit
37 A. ATTHASIT Kasetsart University
Flow with loss : Cascade data
Flow with loss
Total pressure loss coefficient
t ,drop ti tec 2
dynamic i
P P P
P V / 2
Remark :
• Rotor - relative reference
• Stator - fixed reference
Aeropropulsion Unit
38 A. ATTHASIT Kasetsart University
Flow with loss : Total pressure loss coefficient
Flow with loss
t ,drop ti tec 2
dynamic i
P P P
P V / 2
Example for Rotor
t1R t2Rcr 2
1 1R
P P
V / 2
2 2
t2R 1 1R 1 1Rcr cr
t1R t1R t1R
P V PM1 1
P 2P 2P
2
t2R 1Rcr /( 1 )
t1R 2
1R
P M / 21
P 11 M
2
Aeropropulsion Unit
39 A. ATTHASIT Kasetsart University
Flow with loss : Total pressure loss coefficient
Flow with loss
For Rotor
2
t2R 1Rcr /( 1 )
t1R 2
1R
P M / 21
P 11 M
2
For Stator
2
t3 2cs /( 1 )
t 2 2
2
P M / 21
P 11 M
2
How can we evaluate the total
pressure ratio of a stage ?
t 3
t1
P
P
2 1Rcs , 2 2 R cr , 1R 1
t3 t 2 t 2R t1R2 1
t2 2 t2R t1R 1 t1M MM M M M
P P P PP P
P P P P P P
Aeropropulsion Unit
40 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow with loss
Stage calculation
t1 t1R t1 t1RT ,T ,P ,P
t 2 t2R t2 t2RT ,T ,P ,P
&Velocity diagram
t1 t1
m
1 3
21 3 t
1
cr cs
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
uM M 0.7, 1.1, T 22.43K
u
0.09, 0.03
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
tT
Aeropropulsion Unit
41 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow with loss
t1 t1
m
1 3
21 3 t
1
cr cs
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
uM M 0.7, 1.1, T 22.43K
u
0.09, 0.03
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Step 1: Find Triangle "V" at Station 1
Properties
Geometry
V_Compo
V_Compo
(relative)
Properties
(relative)
1T 1a1P
1 1 1V M a 1 1 1u V cos 1 1 1v V sin
1
t1
1
t1 1 M
m TA
P cos MFP
U r
1R 1v r v 2 2
1R 1 1RV u v 1R1R
1
VM
a
t1R 1 1RT f (T ,M , ) t1R 1 1 t1RP g( P ,T ,T , )
Aeropropulsion Unit
42 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow with loss
Step 2: Find "P&T" at Station 2
Properties :
t1 t1
m
1 3
21 3 t
1
cr cs
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
uM M 0.7, 1.1, T 22.43K
u
0.09, 0.03
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
cr , 1R
t 2Rt2R t1R
t1R M
PP P
P
t 2R t1RT T 290.07K
t 2 t1 tT T T
t 2PStill don't know ,let's keep it later!
Aeropropulsion Unit
43 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow with loss
Step 3: Euler's Equation : ?
2 1 2
p t2 t1 1 2
1
u uC (T T ) r tan tan
r u
Euler's Equation :
Then 2 is determined t1 t1
m
1 3
21 3 t
1
cr cs
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
uM M 0.7, 1.1, T 22.43K
u
0.09, 0.03
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Aeropropulsion Unit
44 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Flow with loss
Step 4: Find Triangle "V" at Station 2
22 1 2R 2 2
1
uu u ,v u tan
u
2RV
1 22 2R 2
2
vv U v , tan
u 2V
Step 5: Find "T&P" at Station 2 t1 t1
m
1 3
21 3 t
1
cr cs
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
uM M 0.7, 1.1, T 22.43K
u
0.09, 0.03
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
/( 1 )2
2 22 t2 2 t2R
P t2R
V TT T ,P P
2C T
Aeropropulsion Unit
45 A. ATTHASIT Kasetsart University
Mean radius stage calculation
Step 6: Find the rest at Station 2
2 2 2a ,M ,A
Step 7: Find the rest at Station 3
t3 t3R t3 t3RP ,P ,T ,T ?
3 3P ,T
3 3 3 3 3a ,V ,u ,v ,A
Flow with loss
t1 t1
m
1 3
21 3 t
1
cr cs
T 288.16K ,P 101.3kPa
1000rad / s,r 0.3048m
40 , 1,m 22.68kg / s
uM M 0.7, 1.1, T 22.43K
u
0.09, 0.03
1.4,Cp 1.004kJ / kgK ,R 0.287kJ / kgK
Aeropropulsion Unit
46 A. ATTHASIT Kasetsart University
t 2R t2RT ,P
cr , 1RM
Euler Eq.
2
Mean radius stage calculation - Summary
Flow with loss
t1 t1 m
1 3
1 3 2 1 t
cr cs
T ,P , ,r
, , ,m
M ,M ,u ,u , T
,
t1 t1R t1 t1RT ,T ,P ,Pt 2 t1 tT T T
cs 2,M
Aeropropulsion Unit
47 A. ATTHASIT Kasetsart University
d e 1ug
Design Constrain (Performance control)
Design Overview
Design constrain
Where is the starting point… and the next step …?
Blade Profile Determination
b
c t1Tt1P
13
m1M
cr
cs
Fixed Parameters
(input data)
a mr
3M2u
tT
f
Variable Parameters
Obtained Flow Properties
Aeropropulsion Unit
48 A. ATTHASIT Kasetsart University
Discusion
Design constrain
Preliminary design parameters ….?
a
b
c
d
t1T
t1P
e
mr1
3
m1M 3M
2u
1u
tT
cr
cs
f
g
Nobody can help me ….?!?!
Aeropropulsion Unit
49 A. ATTHASIT Kasetsart University
Engineering Aproach Repeating-Stage, Repeating-Row, Mean-Line Design
R-S, R-R, M-L
Input data
1Mg
D
ec
t1T1
Variables
Flow Properties in each station
Repeating-Stage (Exit condition = Inlet condition)
Repeating-Row (Mirror-image of each row)
Mean-Line Design
Assumption :
- 1=2=3,1=2=3
- u1=u2=u3
- Constant mean radius
- Polytropic efficiency representing stage losses
- Two-dimensional flow (extimate annulus area)
c t1P1utTf
Controled parameter
Simplified
Your life !
Aeropropulsion Unit
50 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
R-S, R-R, M-L
Repeating-row constraint : 1=2=3,1=2=3
2R 1 2v v r v
or
1 2v v r
3 2 3R 2 3 1v v ,v v
And also
Aeropropulsion Unit
51 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
Diffusion Factor
R-S, R-R, M-L
Diffusion factor : High velocity gradient ---> high boundary layer thicnkness ---> high losses
2R 1R 1R
1R 1R
V v v sD 1
V 2V c
csolidity
s
3 2 32R 1R 1R 2 2 12
1R 1R 2 2 1
V v vV v v cos tan tanD 1 1 1 cos ...
V 2V V 2V cos 2
2 1f ( D, , )
Aeropropulsion Unit
52 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
Stage Total Temperature/Pressure Ratio
R-S, R-R, M-L
2 2
t3 1 1s 2 2
t1 1 2
T ( 1)M cos1 1
T 1 ( 1) / 2 M cos
c
c
e /( 1 )
e /( 1 )t3 t3s s
t1 t1
P T
P T
s 1 1 2
s s c
f ( M , , , )
f ( , ,e )
From Euler Eq: p t2 t1 p t3 t1 2 1C (T T ) C (T T ) r( v v )
2 1r v v & Diffusion Factor ?
H
O
w
Aeropropulsion Unit
53 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
Degree of Reaction and Stage Efficiency
R-S, R-R, M-L
( 1 ) /
ss
s
1
1
s s s cf ( , , ,e )
2 2
2 3 p3 22 1 2 1c
3 1 3 1 3 1 t3 t1
V V / 2CT Th h T TR 1 1
h h T T T T T T
2 2
2 3 p
c 2 2
2 3 p
V V / 2C 1R 1
2V V / C
Euler Eq :
Stage Efficiency :
Aeropropulsion Unit
54 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
Stage Exit Mach Number
R-S, R-R, M-L
11 2
Vf ( , )
r
3 3 3 1
2 21 1 1 3 s 1 1
M V / RT T 11
M V / RT T 1 ( 1) / 2 M ( 1) / 2 M
1 1 1 1 1
1 2 1 1 2 1 1 2
V u / cos u / cos 1
r v v u (tan tan ) cos (tan tan )
Inlet velocity/Wheel speed ratio :
Aeropropulsion Unit
55 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
Stage Loading and Flow Coefficient
R-S, R-R, M-L
p t 2 1
2
2 1
C T tan tan
( r ) tan tan
1
1 2
u 1
r tan tan
Flow Coefficient : Axial velocity/rotor speed
Stage Loading : stage work/rotor speed squared
0.3 0.35
0.45 0.55
Aeropropulsion Unit
56 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
General Solution
R-S, R-R, M-L
c( D 0.5, 1,e 0.9 )
Aeropropulsion Unit
57 A. ATTHASIT Kasetsart University
Repeating-Stage, Repeating-Row, Mean-Line Design
General Solution
R-S, R-R, M-L
c( D 0.5, 1,e 0.9 )
Aeropropulsion Unit
58 A. ATTHASIT Kasetsart University
Annulus Area
Flow Path Dimensions
rm
Aeropropulsion Unit
59 A. ATTHASIT Kasetsart University
Conclusion