Compressor Design
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.
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.
Or the load could be a compressor
within a Turbocharger for an
automobile, or a compressor in a jet
engine.
Turbomachines that add energy to the fluid stream
Pump - when the fluid is a liquid or a slurry.
• 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)
Very small to very large pressure rise.
Rotating element is called an impeller.
Fans, Blowers, or Compressors when handling a gas or a vapor.
TPa
TPa
ue
Po
Po
TPa
ua
Po
Pa Po Ai
Jet Propulsion Principle (Thrust)
T=Ai(po-pa)
T: Thrust
Pa: Ambient Pressure
Po: Internal Pressure
ue: Exit Velocity
ua: Mass-average Exhaust Velocity
Steady-Flow
T=mua
.
w1t
Ut
u
ueD
u
c2w1t
w2t
u
Blade Motion
Air MotionAxis of
Rotation
Propeller Theory
Air Velocity (u)
Blade Speed (Ut)
Relative Approach
Velocity (w1t)
Relative Leaving
Velocity (w2t)
Swirling Velocity (u)
Axial Component of
Leaving Velocity (ue)
Leaving Velocity (c2)
Turning Angle ()Ut
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).
Blade
Motion
Air
MotionAxis w1t
Ut
u
Blade
Motion
Air
MotionAxis w1t
Ut
u
Blade speed too high
Flight speed too slow
Operating outside of design
parameters
Poor design: Turning angle
is too large
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
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.
Turboprop
Allison T56 Turboshaft
Turbofan
General Electric CF6 Turbofan
Turbojet
General Electric J79 Turbojet with Afterburner
Turboprop
• Medium-speed
•Moderate-size craft
•High efficiency
•Limited flight speed
•Geared transmission
Turbofan
• Internal Propeller
• Supersonic speeds
• High bypass airflow
• Med/High efficiency
• No gearbox
Turbojet
• High speed
• Mach 4
• Low airflow rate
• Low efficiency
• High op temps
Turbo Engine Comparison
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.
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 Axial-Flow
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.
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
() 15 degrees, specific heat ratio () 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 170m
s D .5m
Urotor 8000rpm 15deg 1.4 Cp 1004m
2
s2
K
kg 1000gm mdot 35kg
s
U
Vin
W1 1
Blade motion
U r UD
2
2
60 s 8000
U 209.44m
s
Wx U Wx 209.44m
s
Step 1.
Create the velocity triangle
and calculate the relative
speed of the rotor blade from
the rotational velocity.
1 atanW x
V in
1 50.934 deg
U
Vin
W1 1
W1 Wx2
Vin2
W1 269.75m
s
Step 2.
Calculate the air to blade
relative velocity and the
angle between the relative
and actual air speed.
2
U w2
Vin
W2
Step 3.
Axial velocity (Vin) does not change.
Calculate relative exit angle(2), then
portion of the relative blade speed
(Uw2). Calculate relative air speed (W2)
2 1
2 35.934 deg
U w2 V in tan 2
U w2 123.214m
s
W 2
V in
cos 2
W 2 209.956m
s
V2 2
U w2Uv2
Vin
W2
Step 4.
Calculate the portion of the relative
blade speed associated with the actual
air velocity (Uv2), the calculate the
actual air speed (V2).
Uv2 Wx Uw2 Uv2 86.226m
s
V2 Vin2
Uv22
V2 190.617m
s
P o2
P o1
T o2
T o1
1The Compressor Pressure
Ratio (CPR) is found from
the isentropic relationship.
To1 Tin
Vin2
2 Cp
To1 314.392K
To1 is calculated from the following equation.
To2 has to be calculated from the specific work
of the compressor stage.
wstage
Tsha ft
mdot
Tshaft mdot
D
2 Uv1 Uv2
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:
Tshaft 754.476J
Power of the shaft is:
Power Tsha ft
2
60 s8000
Power 632.068kW
Uv1 0m
s
No initial tangential component
to the inlet velocity.
wstage
Power
mdot
wstage 1.806 104
J
kg
Specific work of
the stage is then:
To2 To1
wstage
Cp
CPRTo2
To1
1
Now To2 can be calculated from the specific work
To1, and the conversion factor.
To2 332.38K
Finally, the Compressor Pressure Ratio can be
calculated!!!To2 To1
wstage
Cp
CPRTo2
To1
1
CPR 1.215
The answer is:
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