Illustration of working of gas turbine engines:
The basic operation of the gas turbine is similar to that of the steam power plant except that air is used instead of water.
Fresh atmospheric air flows through a compressor that brings it to higher pressure.
Energy is then added by spraying fuel into the air and igniting it so the combustion generates a high-temperature flow.
This high-temperature high-pressure gas enters a turbine, where it expands down to the exhaust pressure, producing a shaft work output in the process.
The turbine shaft work is used to drive the compressor and other devices such as an electric generator that may be coupled to the shaft.
The energy that is not used for shaft work comes out in the exhaust gases, so these have either a high temperature or a high velocity.
Thrust Equation for a Gas Turbine Engine
Thrust produced by a turbojet engine is determined by 3 things:
a) The change is momentum experienced by air flowing through the engine.
b) The momentum of fuel.
c) The force caused by the difference in pressure across the exhaust nozzle to multiply by area of nozzle.
There are 2 types of thrust:-
a) Net thrust &
b) Gross Thrust
a) Net Thrust: The thrust produced by a turbojet engine in flight. Net thrust considers a momentum of air entering and leaving the engine.
b) Gross Thrust: The thrust produced by a turbojet engine when the engine is static or not moving. Gross thrust consider the inlet momentum be zero.
Both weight and mass may be expressed in terms of pounds, but they are not the same. Mass is the amount of matter in an object and is not affected by gravitational pull of earth. Weight on the hand is the effect of gravity on mass.
Mass = Weight (Pounds)
Acceleration due to gravity.
Mass = Weight (Pounds)
32.2 fps 2
Momentum is the product of the mass of an object multiplied by its velocity. The momentum of air and fuel passing through a gas turbine engine is found by dividing their weight in pounds per second by the acceleration due to gravity or 32.2 feet per second. This is then multiplied by the velocity of gases leaves the engine.
|Momentum of air and fuel leaving engine = (Wa + Wf)/ g x V2|
Wa = Weight of air flowing through the engine is pounds per second.
Wf = Fuel flow in pounds per second.
g = Constant for acceleration due to gravity of 32.2 feet per second2.
V 2 = Velocity of exhaust gases in feet per second.
The fuel is carried in the aircraft. So it has no initial velocity relative to the engine. The momentum of air and fuel entering of the engine is
Momentum of air and fuel entering engine = Wa/g x V1
V 1 = Velocity of incoming air in feet per second. This is the speed of aircraft.
The portion of thrust produced by the change in momentum of air and fuel passing through the engine is the sum of the change in momentum of air and change in momentum of fuel.
The formula for this portion of thrust is
F = Wa /g (V2 – V1) + Wf /g(V2)
In some practical problems, the mass of the fuel flow is omitted, as it is quite small in comparison with the mass of airflow.
Air Pressure at Nozzle
Many subsonic jet nozzles operated in a chocked condition. This means that air flowing through the convergent section of the exhaust duct reaches the speed of sound and can no longer accelerate. The energy that would have caused acceleration now increases the pressure and crates component of thrust by the difference between the exhaust pressure and pressure of air surrounding the exhaust nozzle.
This component of thrust may be found by this formula.
F = A j (P2 – Pam)
Aj = Aera of extent jet nozzle in square incher.
P2 = Static air pressure at the jet nozzle discharge in pounds per square inch.
Pam = Static pressure of ambient air at the jet nozzle in pounds per square inch.
The total net thrust produced by a turbojet or turbofan engine may be found by combining of the two type of thrust discussed into a single formula.
Net thrust (Fn) = Thrust caned by change in momentum of the air
Thrust caused by changing momentum of fuel
Thrust caused by pressure drops net nozzle.
Fn = Wa/g (V2 – V1) + Wf /g(V2) + Aj (P2 – Pam)
Momentum of air Momentum of fuel Pressure drop