Page 150 - Advanced Thermodynamics for Engineers, Second Edition

6.7 PROBLEMS 137

6.6 CONCLUDING REMARKS
A new method for assessing the potential thermal efficiency of heat engines has been introduced. This
is based on the engine operating at its maximum power output, and it is shown that the thermal
efficiency is significantly lower than that of a Carnot cycle between the same temperature limits. The
loss of overall efficiency is due to the external irreversibilities that are present in all devices producing
power output – even electrical devices. It has been shown that this approach approximates the thermal
efficiency achieved by actual power plant.
It has been shown that a combined cycle power plant cannot operate at a higher thermal efficiency
than a single cycle plant between the same temperature limits. However, the use of two cycles enables
the temperature limits to be widened, and this is the reason better efficiencies are achieved.
Finally, an example was given of a nonreversible gas turbine with a heat exchanger, called an IFGT
cycle.
The model derived could be used to optimise the operational parameters and forecast performance
of practical IFGT configurations and choices. Furthermore, relevant equations can be used to optimise
the performance of the particular IFGT cycles under a variety of constraints, including: (1) seeking the
optimal pressure ratio to achieve either maximum power output or maximum efficiency, with all other
parameters held constant; (2) finding the optimal set of values of the various thermal conductances
under the constant total heat conductance criteria. The FTT approach shows that IFGT cycles are most
efficient under low compression ratio ranges (2.0–5.0) and appropriate for integrating micro gas
turbine technology for low power output applications. The optimal total pressure ratio, p c , under
maximum power output is always higher than that under maximum cycle thermal efficiency. The IFGT
cycles share common characteristics with regenerated Brayton cycles and intercooled, regenerated
Brayton cycles such that the dimensionless power output, efficiency and the corresponding optimal
total pressure ratio are highest when the heat transfer effectiveness of the hot- or the cold-side heat
exchanger, the pressure recovery coefficient, isentropic efficiencies of the gas turbine and the
compressor and the heat reservoir inlet temperature ratio are high. It was also shown that the optimal
total pressure ratio, p c , under the maximum cycle thermal efficiency decreases with the increase of
heat transfer effectiveness of the HTHE.

6.7 PROBLEMS

P6.1 Explain why the Carnot cycle efficiency is unrealistically high for a real engine. Introducing
the concept of external irreversibility, evaluate the efficiency of an endoreversible engine at
maximum power output.
Consider a heat engine connected to high-temperature reservoir at T H ¼ 1200 K and a low
temperature one at T C ¼ 300 K. If the heat transfer conductance from the reservoirs to the
engine are in the ratio (UA) H /(UA) C ¼ C H /C C ¼ 2, evaluate the following:
1. the maximum Carnot cycle efficiency;
2. the work output of the Carnot cycle;
3. the engine efficiency at maximum power output;
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4. the maximum power output, W=C H and
5. the maximum and minimum temperatures of the working fluid at maximum power output.