Notes on Jet Propulsion
Thrust
The general thrust equation for rocket engines is:
F = (mdot V)e + (pe – p0)Ae
Thrust is generated by the propulsion system of a vehicle. It's a force that's generated through the acceleration of a mass of gas.
For a moving fluid (such as air in the case of the jet vehicle project), we use the mass flow rate which describes the amount of mass moving through a given plane over a certain amount of time. The units are mass/time, and it is equal to the density (r) times the velocity (V) times the area (A). It's usually written as mdot.
mdot = rVA
Nozzle
The nozzle determines the exit velocity for a given pressure and temperature. The geometry of the nozzle sets the mass flow rate. Consequently, the nozzle design determines the thrust of the propulsion system.
The velocity of a fluid increases when the area decreases. This is only true when the fluid is subsonic and incompressible. When a fluid is incompressible, the density (\roh) is constant. The fluid operates below the speed of sound. Mach .4 or below
In a supersonic nozzle, the velocity of the fluid increases as the area increases. For fluids above Mach .5 the density begins to change. Velocity and pressure are inversely proportional. When the velocity increases, the pressure decresaess.
A rocket nozzle is shaped like a C-D (converging-diverging) nozzle. The idea is that the fluid in the chamber, is at rest. (In the jet vehicle project, the chamber is the pipe that connects the balloon to the nozzle.) In a C-D nozzle, the converging section will accelerate the fluid to a sonic flow. The fluid is at a sonic flow when it reaches the throat. The diverging section accelerates the fluid to a supersonic flow.
Nozzle expansion
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ideal expansion flow: pressure at the exit of the nozzle equals atmospheric pressure
- in rockets, this is not always possible becuase the atmospheric pressure is something we can't ocntrol unless the vehicle travels at a constant altitude. In most cases, the flow will be in over-expanded or under-expanded conditions.
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over - exit pressure less than atmospheric pressure
- the idea is to not let the fluid expand too much
- in fighter jets, the design the airframe is such a way that the exit jet does not create damage to aircraft components
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under - exit pressure greater than atmospheric pressure
- this is often used in rockets where the goal is to create the maximum amount of force