AE 1350

Lecture Notes #13

Topics to be discussed

• Propellers

• Gas Turbines– Turbojet– Turboprop– Turbofan

• Rockets

How does a propeller work?

It captures a stream of air molecules, adds energy to the particles.

Particles approach the propeller with low velocity.

They leave with higher velocity, and energy.

This change in momentum of the particles is caused by the rearward force exerted by the propeller on the particles.

There is an equal and opposite reaction - the particles exert a forwardforce on the blades. This is called thrust.

As the propeller turns..

V V+v V+2v

Streamlines contract as they approach the propeller.Velocity of the particles steadily increases.

Thrust Generated

V V+v V+2v

Mass flow rate = A (V +v) where A is the propeller disk area.Momentum flow rate = mass flow rate times velocityThrust = Rate at which Momentum flows out-

Rate at which momentum flows in = A(V +v) (V +2v) - A (V +v) V = 2A(V +v)v

Thrust is increased if the disk area A is large, and/or if the excess velocity v is large.

Power Consumed

V V+v V+2v

Mass flow rate = A (V+v) where A is the propeller disk area.Energy flow rate = 1/2 times (mass flow rate) times (velocity squared)Rate at which energy is added to the fluid = Rate at which energy flows out- Rate at which momentum flows in

= 1/2A(V+v) (V +2v)2 - 1/2 A (V +v) V2

= 2 A(V + v)2 v = T(V +v)

Notice that power consumed will be high for a given thrust T and forward velocity V, if v is high.

Propeller Thrust vs. Power ConsumedT = 2A (V +v)v

P = T(V +v) = TV + Tv

The first term TV is useful work done by the propeller to

overcome drag.

The second term, Tv, called induced power, represents excessenergy we dump into the wake, as the propeller accelerates theflow a higher velocity.

To keep the power minimum, this excess energy must be kept small.

Propulsive efficiency = Useful Power/Total Power

= TV /(TV +Tv) = V /(V +v)

where T = 2A(V +v)v

Thumb Rule the propeller designer: Keep disk area A as large as possible, v as small as possible.

There is a limit to the Disk Area•If we make the disk area too large, the blade radius and diameter will be high.

•Tip will spin at too high a speed.

•If cruise speed is also high, shocks will form on the blades.

•Additional power will be needed to overcome the drag on theblades caused by the shock waves.

•Noise will also go up.

•These factors have limited the use of propellers to aircraft that have relatively lower thrust requirements or low subsonic cruise speeds (Mach 0.6 or less).

How is the propeller or fan turned?

• With a – piston engine (as in a car)

or a– gas turbine engine

Radial Piston Engines

These engines now belong in a museum...

Gas Turbine Engines - Turbofan

The fan acts like a propeller, provides the majority of thrust.

Turbine EnginesHow They Work

Turbine engines have four major sections:

Gearbox — uses shaft power to turn a generator and other accessories.

Compressor — draws in outside air and increases the pressure of the air.

Combustor — mixes fuel with the air. This mixture is ignited and directed to the turbine section.

Turbine — extracts energy from the heated air to turn the fan, compressor, and gearbox via the common shaft and produces direct thrust through the exhaust nozzle.

Low Bypass Ratio TurbofanJT8D CharacteristicsFan tip diameter: 54.0 inchesLength, flange to flange: 168.6 inchesTakeoff thrust: 21,000 pounds of thrustBypass ratio: 1.74-to-1Overall pressure ratio: 18.2 to 19.4Fan pressure ratio: 1.91

Engine ModelsJT8D-standardJT8D-217/219

Planes Powered by JT8DBoeing 727Boeing 737-100/-200McDonnell Douglas DC-9Boeing MD-80

High Bypass Ratio TurbofanFan tip diameter: 112 inchesLength, flange to flange: 191.7 inchesTakeoff thrust: 86,760 - 98,000 pounds

Bypass ratio: 5.8-to-1 to 6.4-to-1Overall pressure ratio: 34.2 - 42.8Fan pressure ratio: 1.70 - 1.80

Engine ModelsPW4084PW4090PW4098

Planes Powered by PW4000Boeing 777-200/-300

Turbojet Engines

The fan produces very little thrust. Remember from the propeller theory that thrust depends on disk area.

Most of the thrust is produced by the jet coming out of the nozzle.

Assuming that the jet exits the nozzle at ambient pressure,

T = Mass Flow Rate times change in velocity= Mass flow rate times (Exit Velocity - Inlet Velocity)

Turbojets dump a lot of excess energy into the exhaust and are inefficient.

Turboshaft EnginesThe engine core operates in the same manner as in turbojet or turbofan engines.

Turbines turn the engine shaft.

The power from the engine shaft may be used to spin

a propeller (turboprop),

or a rotor (helicopter),

or a power generator

Core

Gear Box

PropellerorRotor

Supersonic Combustion Ram JetSCRAMJET Engines

In this engine, compressors are not used.

Shock waves in front of the aircraft and inside the inletslow down the flow and increase the pressure.

The flow inside the entire engine, including the compressor, is supersonic.

An aerospace plane will use a SCRAMJET engine.

Jet Engines and Piston Engines Need Air...

• Jet engine and piston engine aircraft carry only the fuel.

• They need air (or oxidizer) for combustion of the fuel and generation of energy.

• For this reason, these are called air-breathing engines.

• These devices stop working outside the atmosphere.

• In our next lecture, we will study rocket engines.

Solid and Liquid Fuel Rocket Motors

Liquid Fuel Rocket Motorhttp://www.execpc.com/~culp/space/propulsn.html

• Uses separate liquid fuel and oxidizer, which are combined only at the moment of combustion.

• Pumps are required to get the fuel & oxidizer to the motor quickly enough to develop desired thrust.

• This makes liquid fuel rockets more complicated.

• Liquid fuel rockets can be turned off and then turned on again.

• On the space shuttle, they can be throttled for more or less thrust.

• So liquid fuel rockets are more controllable.

Rocket Motor Thrust

Thrust = (Mass Flow Rate) * Vjet

+ (pexit - p) Aexit

Impulse

• Thrust varies with time.

• Rockets are instead rated according to their impulse:

EndsFiring

startsFiring

dtThrust_

_

Impulse

The above integral is done over the time period when the rocketstarts firing and when it stops.