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5: The Brayton Cycle

EFFICIENCY Efficiency is an expression of the degree of perfection.  

  Efficiency is also the ratio of the Useful Output to the Input.  

Thermal Efficiency is the ratio of the rate of addition of kinetic energy to the working fluid to the rate of addition of heat in the form of heat of reaction of the fuel.  

For a single-flow jet engine (only one exhaust),   where qR is the heat released per unit mass of fuel consumed.

For a shaft-powered engine,   where is the shaft power.  

Propulsive Efficiency is the ratio of thrust power to the rate of addition of kinetic energy.   I

f we ignore the pressure thrust term, and assume that f is very much smaller than 1,      

Overall efficiency is the product of these two efficiencies.  

Note: 1. Thermal efficiency depends on a) thermodynamic cycle b) combustion efficiency (how much of the heat is really released?)   2. Propulsive efficiency depends on how close the exit velocity is to the flight velocity. We can easily show that this efficiency reaches 1.0 when the two velocities are equal, but then the thrust is zero. To get a given thrust with high propulsive efficiency, it is thus better to accelerate a large mass flow rate through a small velocity increment, than to accelerate a small mass flow rate through a large velocity increment.  

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