Jet Propulsion and Compressor Design

NASA's X-43A

Keith LarsonIC Engines and Propulsions Systems

Spring 2005

Professor

Dr. Chiang Shih

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.

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

Turbine Classifications* Hydraulic Turbines - The working fluid is WATER.

- Flow is incompressible.

* Gas and Steam Turbines - Density of the working fluid may change significantly.

• 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.

Further Classification

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

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

.

Acceleration of a stream of air through a Propeller

Engineu ue

Thrust per Unit Energy Consumption (Rocket vs. Propeller)

Propeller Thrust Ratio

.T=ma(ue-u)

. .E

ma

e

uc2

2

ua2

2

.TE

2 e

ue u

Assume a best thermal efficiency of 40%, the maximum possible value of propeller thrust ratio becomes.

.TE

2

5u

T

T

propeller

rocket

1000

u

Rocket

Tmpuer• • •Emp

uer2

2

•TE

2

uer2

Rocket Thrust Ratio

Estimate ratio of propeller and rocket thrusts

T

T

propeller

rocket

uer

5u

Assume that the rocket exhaust velocity is 5000m/s.

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.

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 Motion

Axis w1t

Ut

u

Blade Motion

Air Motion

Axis 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 1004m2

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 Vin

2 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 w2U v2

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 Uv2

2 V2 190.617m

s

P o2

P o1

T o2

T o1

1

The 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

Tshaft

mdot

Tshaft mdotD

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 Tshaft2 60 s

8000

Power 632.068kW

Uv1 0m

s

No initial tangential component to the inlet velocity.

wstagePower

mdot

wstage 1.806 104J

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:

Lockhead SR-71 Blackbird

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.

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.