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The Brayton Cycle: The easiest way to
understand this cycle is to break it into the 4 different parts of the
jet engine. The engine consist of a compressor, combustion chamber,
turbine, and nozzle. The steps of the cycle are:
- Compressor does work on the air. (Adiabatic
compression)
- The burner add heat to the air (Constant pressure
heat addition)
- The turbine takes work out of the air and
uses it to run the compressor. (Adiabatic expansion)
- The air flows through the nozzle and leaves
the engine at a higher speed than the air in the atmosphere. Since
step 4 occurs in the atmosphere and the air is not recycled through
the system, the nozzle is not included in calculations.
Below is a schematic of the cycle.
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The thermal efficiency is the work of the compression
and the work of the expansion divided by the negative heat.
Closed System: eff = (WS,AB
+ WS,CD ) / -QBC
Substitute the work and heat with DeltaH from the energy
balance.
If assuming ideal gas: DeltaH = CpDeltaT
The efficiency equation can be simplified to the following
equation using algebra:
eff = 1-[(TD - TA)
/ (TC - TB)]
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There are three types of efficiencies that are important for
gas turbine engines. They are
propulsive, thermal and
overall efficiency. The thermal efficiency is defined
as:
Thermal Efficiency = hp output of engine/ hp value
of fuel consumed
where, the hp output of the engine is equivalent to the total
work of the engine, and the hp value of the fuel consumed is equivalent to the
heat added to the air in the system. The most important factors that affect
the thermal efficiency are:
The best thermal efficiencies that have been observed for normal jet engine
processes are in the range of 45%-50%. This is observed in very large engines
with a 30 to 1 compression ratio and turbine inlet temperatures of 2,500 to
3,000 degrees Fahrenheit. The ideal case results from the conditions of a turbine
inlet temperature of 3,000 deg F and a 32 to 1 compression ratio. These conditions
are desirable because expansion in the turbine and combustor sections is greatest
when high pressure and large amounts of heat are combined.
The individual efficiencies of the turbine and compressor are also important
for the overall performance of the engine. Typical efficiencies for large-size,
modern jet engines usually lie in the range of mid to high eighties. The most
energy efficient conditions of the compressor and turbine sections in a gas
turbine engine occurs when compression temperatures are low since this allows
for a greater temperature rise in the combustor and, therefore, the greatest
expansion. Ideal compressor efficiency occurs when the compressor produces the
maximum pressure with the minimum temperature rise. The ideal turbine extracts
the most work for the lowest fuel consumptions.
The overall efficiency is the product
of the thermal efficiency and the propulsive efficiency, which is defined by:
Peff = thrust power/ thrust power + kinetic energy wasted
