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: