Aviation and the Global Atmosphere

Aviation and the Global Atmosphere
Aviation and the Global Atmosphere
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7.4.1.1. Thermal Efficiency
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One of the most fundamental measures needed to assess the effectiveness of a gas turbine is its ability to convert the chemical energy of the fuel into mechanical
work-the thermal efficiency of the engine (i.e., h therm = power to the gas stream/ energy input rate). The precise derivation of this parameter requires a knowledge of
the details of flows within the engine, including air used inside the engine to cool hot parts. For present purposes, however, a good estimate of the constraints and
potential of the engine can be obtained by neglecting such minor flows and by further assuming that the working fluid throughout the engine retains the same
properties as air at room temperature throughout the cycle. The compressor and turbine are inevitably less than perfect, and their performance is described by
efficiencies (h comp and h turb , respectively). This simple treatment assumes that h comp = h turb = 90%; these are plausible "state-of-the-art" values. The two properties
that affect gas turbine thermal efficiency are T 4 /T 2 -the ratio of temperature leaving the combustor (i.e., the turbine inlet temperature) to that of the air entering the
engine-and the overall pressure ratio between atmospheric pressure and peak pressure within the engine.
Taking first the effects of variations in T4 /T2 at typical conditions in the cruise phase of a modern civil aircraft (Mach 0.85 at 10.7-km altitude), the inlet temperature, T2 ,
sensed by the engine for standard atmospheric conditions is 250 K. The upper limit on temperature, T4 , would be reached if sufficient hydrocarbon fuel were burned to
consume all the oxygen (stoichiometric combustion; see Figure 7-8). This temperature would be about 2590 K, though this value depends to some extent on the
pressure ratio of the engine and the efficiency of the components. These values give T4 /T2 ª 10.3. For a mid-1990s engine the value of T4 at cruise is about 1400 K,
whereas in the mid-1970s a value of about 1250 K would have been more typical. For these combinations of air inlet temperature, and turbine inlet temperature the
ratio T4 /T2 would be 5.6 and 5.0, respectively. Figure 7-8 shows, for these three examples, the thermal efficiency of a gas turbine as a function of pressure ratio for
cruise at Mach 0.85 at 10.7 km. The solid lines are for compressor and turbine efficiencies of 90% and are labeled with the temperature ratio T 4 /T 2 . The broken line is
for ideal compressors and turbines (having h comp = h turb =100%); in this case, the thermal efficiency is a function of pressure ratio only.
Figure 7-8 also shows that for high thermal efficiency, the internal pressure ratio of the engine must be moderately high; for new large engines, the value is around 40
at peak throttle settings of take-off and climb. In addition to "internal" compression of air (by the compressor), the aircraft's forward speed introduces a pressure rise of
1.6 times atmospheric pressure at Mach 0.85, giving an overall pressure ratio of about 64. Increasing the internal pressure ratio much beyond this value raises the
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