Modern Engineering Thermodynamics

13.17 Aircraft Gas Turbine Engines 499
When the isentropic efficiencies of the compressor and prime mover are taken into account, the Brayton cycle
thermal efficiency becomes
ðη T Þ Brayton =
_W s ð
pm η sÞ pm − j _W s
c / ð η sÞ c j
_Q H
ð Þ pm
− ðT 4s − T 3
ð
= T 1 − T 2s Þ η s
T 1 − T 4
Þ/ ðη s
where T 4 = T 3 +(T 4s – T 3 )/(η s ) c . It is clear that this efficiency has a positive value only if
or
ðη s Þ pm ðη s Þ c ≥ ðT 4s − T 3 Þ/ðT 1 − T 2s Þ = T 4s /T 1
ðη s Þ pm
ðη s Þ c
≥ ðT 3 /T 1 ÞPR ðk−1Þ/k = ðT L /T H ÞPR ðk−1Þ/k
Þ c
= ðT 3 /T 1 ÞCR k−1 = ðT L /T H ÞCR k−1 (13.28)
13.17 AIRCRAFT GAS TURBINE ENGINES
The major function of an aircraft jet engine is to produce a high-velocity exhaust jet whose thrust is large
enough to propel the aircraft. The engine’s thrust T is given by
T = _mðV exhaust − V inlet Þ/g c (13.29)
where both the inlet and exhaust velocities are measured in a coordinate system fixed to the engine, and the
mass flow rate is _m = _m fuel + _m air = _m exhaust . A jet engine needs to produce only enough net output power to
drive the aircraft’s accessories (fuel pump, hydraulics, generator, etc.), and consequently, it need not have a very
high thermal efficiency (the exhaust kinetic energy is considered to be lost energy in a thermal efficiency analysis).
This was an ideal application for the inherently inefficient gas turbine engine of the 1930s. The pressures of World
War II caused intense research and development in aircraft gas turbine turbojet engine development. The first successful
turbojet aircraft was the German Heinkel-178, which flew for the first time on August 27, 1939. The engine
weighed 800 lbf (364 kg) and produced a thrust of 1100 lbf (4890 N) at 13,000 rpm. As a result of intense wartime
technological development, axial flow compressors with pressure ratios of 3.0 and isentropic efficiencies of
75−80% were available by the end of World War II.
Modern aircraft gas turbine engines have compressor pressure ratios as high as 25, and ceramic-coated super
alloys have allowed turbine inlet temperatures to approach 3000 R. Their turbine isentropic efficiencies are typically
in the range of 85 to 95%, and their compressor isentropic efficiencies usually fall in the range of 80 to
90%. Figure 13.46 illustrates the construction of a modern gas turbine engine.
FIGURE 13.46
World class design. The GP7000 was designed by a 50/50 joint venture between GE and Pratt & Whitney for the Airbus A380.
(Source: United Technologies, Pratt & Whitney Aircraft.)