1. Jet Propulsion and Compressor Design
NASA's X-43A
Keith Larson
IC Engines and Propulsions Systems
Spring 2005
Professor
Dr. Chiang Shih

2. Fluid Machinery
Positive Displacement
• Working fluid is confined
within a boundary.
•Energy transfer is by volume
changes due to the
movement of the
boundary.
Dynamic
• Working fluid is not confine
within a boundary.
• Energy transfer is by dynamic
effects of the rotor on
the fluid stream.

3. Dynamic Machine
A.K.A. Turbomachines
* Radial-Flow - Also called Centrifugal.
- Radial flow path.
- Large change in radius
from inlet to outlet.
* Axial-Flow - Flow path nearly parallel
to the axis of rotation.
- Radius of the flow path
does not very significantly.
* Mixed-Flow - Flow path radius changes
only moderately.

4. Turbomachines that extract energy from the fluid stream
Turbines
Turbines use Vanes, Blades, or Buckets attached to the
turbine shaft.
This assembly is called the Rotor, Wheel, or Runner.
Bourn, Cambridgeshire, England
Colvin Run Mill
near Dranesville,
Virginia

5. Turbine Classifications
* Hydraulic Turbines - The working fluid is WATER.
- Flow is incompressible.
* Gas and Steam Turbines - Density of the working fluid
may change significantly.
Further Classification
• Impulse Turbines - Driven by one or more high-speed free jets.
- Each jet is accelerated in an external nozzle.
- Fluid acceleration and pressure drop is
external to the blades.
• Reaction Turbines - Part of the pressure change takes place
externally and part takes place within
the moving blades.

6. The turbine extracts
energy from the fluid
stream and converts it
into mechanical energy,
which is then transmitted
through a shaft to some
load.
The Steam Turbine Generator
Satsop Development Park

7. Or the load could be a compressor
within a Turbocharger for an
automobile, or a compressor in a jet
engine.

8. Turbomachines that add energy to the fluid stream
∗ Pump - when the fluid is a liquid or a slurry.
• Very small to very large pressure rise.
• Rotating element is called an impeller.
∗ Fans, Blowers, or Compressors when handling a gas or a vapor.
• Fans - generally have a small pressure rise (< 1 inch water)
• Blowers - moderate pressure rise (1 inch of mercury)
• Compressors - very high pressure rise (up to 150,000 psi)

9. Jet Propulsion Principle (Thrust)
Pa
T
T
Po
Pa
T: Thrust
Po
Pa: Ambient Pressure
ue
Steady-Flow
T
T=Ai(po-pa)
Po
Pa
Pa
Ai
Po: Internal Pressure
ue: Exit Velocity
.
T=mua
Po
ua
ua: Mass-average Exhaust Velocity

10. Thrust per Unit Energy Consumption (Rocket vs. Propeller)
Engine
u
ue
Acceleration of a stream of air through a Propeller
Propeller Thrust Ratio
.
T=ma(ue-u)
.
2 ⋅η e
T ≅ ue + u
E
. 
.
E
2
2
ma uc
ua

−
2 
ηe  2
Assume a best thermal
efficiency of 40%, the
maximum possible value of
propeller thrust ratio becomes.
2
T ≅ 5u
.
E

11. Rocket
2
•
T≅mpuer
• mp⋅
E≅ •
u er
2
2
T ≅ uer2
•
E
T
p
o
r
l
e
T
o
r
e
k
c
t
Rocket
Thrust Ratio
Estimate ratio of propeller and rocket
thrusts
u er
Assume that the
T
5u
≅
p
o
r
l
e
rocket exhaust
T
velocity is 5000m/s.
o
r
e
k
c
t
1000
≅ u

12. Summary of Propeller and Rocket Thrust
⇒ For Aircraft propulsion the big advantage of using a propeller is
that less fuel must be carried on board.
• The rate of airflow through the propeller can be as much as
three orders of magnitude larger than the rate of fuel
consumption of the driving engine.
⇒Propulsion using a propeller has much better efficiency when
compared to propulsion with a rocket.
• The aircraft using a propeller can travel much greater
distances before having to refuel.

13. Propeller Theory
Air Velocity (u)
Axis of
Rotation
Air Motion
Blade Speed (Ut)
w1t
u Relative Approach
Velocity (w1t)
Ut
Relative Leaving
Velocity (w2t)
Blade Motion
Swirling Velocity (uθ)
u
Dβ
w2t
w1t c2
Ut
u
ue
Axial Component of
Leaving Velocity (ue)
Leaving Velocity (c2)
Turning Angle (∆β)

14. Limitation of the Propeller in Propulsion
In order to maintain good flow over the blade certain
conditions must be meet.
1. The relative approach angle and the blade leading
edge angle must be close to prevent flow
separation from the blade.
2. The turning angle must be keep quite small, or the
flow will also separate from the blade.
3. The relative approach velocity must not be too
close to the speed of sound. This is to prevent
shock waves from forming on the blade.
Thus conventional propellers are used for flight speeds well below
the speed of sound; usually at or below 135 m/s (300 mph).

15. Axis
Air
Motion w1t
Ut
Blade
Motion
Blade speed too high
u
Flight speed too slow
Operating outside of design
parameters
Axis
Poor design: Turning angle
is too large
Air
Motion
w1t
u
Ut
Blade
Motion

16. The Importance of the Compressor/Turbine in Modern Flight
It was not until 1939 that a compressor, combuster, and turbine
were coupled together to create the first turbo engine for aircraft
propulsion.
Air Inlet
Exhaust
Gas Out

17. 1. The turbine engine made supersonic flight possible in aircraft
2. Reduced the cost of air travel.
3. Lead to great improvements in aircraft safety.

18. Turboprop
Allison T56 Turboshaft

19. Turbofan
General Electric CF6 Turbofan

20. Turbojet
General Electric J79 Turbojet with Afterburner

21. Turbo Engine Comparison
Turboprop
Turbofan
Turbojet
• Medium-speed
• Internal Propeller
• High speed
•Moderate-size craft
• Supersonic speeds
• Mach 4
•High efficiency
• High bypass airflow
• Low airflow rate
•Limited flight speed
• Med/High efficiency
• Low efficiency
•Geared transmission
• No gearbox
• High op temps
NOTE: Due to the ram compression due to flight speed, the optimum
compressor pressure ratio (CPR) goes to zero around Mach 4.
CPR 30:1 for subsonic flight.
CPR 10:1 @ Mach 2.
Compressor not needed at Mach 4; Ramjet.

22. Comparison of the Axial-Flow and Radial-Flow Compressors
Axial-Flow compressors do not significantly change the direction of
the flow stream, thus Axial-Flow Compressor allows for multiple
stages. Radial-Flow Compressors can not be staged.
While the Radial-Flow Compressor has a larger Compressor
Pressure Ratio (CPR) per stage, the multi-stages of the Axial-Flow
compressor allows for a larger overall CPR.
The frontal area for a given air flow rate is smaller for an AxialFlow Compressor than for a Radial-Flow Compressor.
The Axial-Flow Compressor has a higher efficiency.
Disadvantages are the higher cost to manufacture the Axial-Flow
Compressor, and the Radial-flow Compressor is more durable than
the Axial-Flow Compressor.

24. Example Problem
Given a first single stage of an Axial Compressor with the following
conditions: ambient pressure (Pin) 1 atmosphere, ambient
temperature (Tin) 300K, aircraft cruising speed (Vin) 170m/s, median
blade diameter (D) 0.5m, rotor rpm (Urotor) 8000rpm, turning angle
(∆β) 15 degrees, specific heat ratio (γ) 1.4, air mass flow rate (mdot)
35kg/s, and (Cp) conversion factor 1004 m2/s2*K, calculate the first
stage Compressor Pressure Ratio (CPR).
Pin := 1atm
Tin := 300K
Vin := 170
m
s
D := .5m
2
Urotor
8000rpm
kg := 1000gm
∆β := 15deg
mdot := 35
kg
s
γ := 1.4
Cp := 1004
m
2
s ⋅K

25. Step 1.
Vin
β1
W1
U
Blade motion
U
Create the velocity triangle
and calculate the relative
speed of the rotor blade from
the rotational velocity.
D 2⋅ π
U := ⋅
⋅ 8000
2 60⋅ s
rω
U = 209.44
W x := −U
m
s
W x = −209.44
m
s

26. Vin
β1
Step 2.
W1
Calculate the air to blade
relative velocity and the
angle between the relative
and actual air speed.
U
W 1 :=
2
Wx
+ Vin
2
W x 
β 1 := atan 

V in 

W 1 = 269.75
m
s
β1 =−
50.934 deg

27. Step 3.
W2
Vin
β2
U w2
β 2 := β 1 + ∆β
β 2 = −35.934 deg
Axial velocity (Vin) does not change.
Calculate relative exit angle(β2), then
portion of the relative blade speed
(Uw2). Calculate relative air speed (W2)
( 2)
U w2 := V in⋅ tan β
U w2 = −123.214
m
s
W 2 :=
W
2
V in
( )
cos β 2
= 209.956
m
s

28. Step 4.
V2
W2
Vin
U v2
β2
U w2
Calculate the portion of the relative
blade speed associated with the actual
air velocity (Uv2), the calculate the
actual air speed (V2).
Uv2 := W x − Uw2
V2 :=
2
Vin
+ Uv2
Uv2 = −86.226
2
V2 = 190.617
m
s
m
s

29. The Compressor Pressure
Ratio (CPR) is found from
the isentropic relationship.
γ
P o2
P o1
 T o2 
γ −1


T o1 

To1 is calculated from the following equation.
To2 has to be calculated from the specific work
of the compressor stage.
To1 := Tin +
Vin
2
2⋅Cp
To1 = 314.392 K

30. Specific work of the stage is
calculated from the torque of the
shaft, angular velocity of the blade,
and mass flow rate of the air.
Torque of the shaft is:
Uv1
0
m
s
No initial tangential component
to the inlet velocity.
Power of the shaft is:
wstage
Tshaft := mdot⋅
D
2
Tshaft⋅ ω
mdot
⋅ ( Uv1 − Uv2)
Tshaft = 754.476 J
 2⋅ π ⋅ 8000 
Power := Tshaft⋅ 

 60⋅ s

Power = 632.068 kW

31. wstage :=
Specific work of
the stage is then:
Power
mdot
4
wstage = 1.806 × 10
J
kg
Now To2 can be calculated from the specific work
To1, and the conversion factor.
To2 := To1 +
CPR :=
wstage
 To2 
Cp
γ
γ −1
To2 = 332.38 K

32. Finally, the Compressor Pressure Ratio can be
calculated!!!
wstage
To2 := To1 +
Cp
γ
γ −1
C
P
R
 To2 
CPR := 

 To1 
The answer is:
=
1
.
2
5

33. The engines on the blackbird
are turbojets and are used as
such up to about Mach 4; when
the air flow is bypassed around
the compressor and the engines
become ramjets.
Lockhead SR-71 Blackbird

34. NASA X-43A
This is where we are today. The X-43A is an
experimental aircraft that uses a scramjet (supersonic
ramjet) for its propulsion. The X-43A has reach speeds
of about Mach 10.