An ideal gas turbine cycle with many stages of compression...

An ideal gas turbine cycle with many stages of compression and expansion and a regenerator of 100 percent effectiveness has an overall pressure ratio of 10. Air enters every stage of compressor at $290 \mathrm{~K}$, and every stage of turbine at $1200 \mathrm{~K}$. The thermal efficiency of this gas-turbine cycle is (a) 36 percent (b) 40 percent (c) 52 percent (d) 64 percent (e) 76 percent

An ideal gas turbine cycle with many stages of compression and expansion and a regenerator of 100 percent effectiveness has an overall pressure ratio of 10. Air enters every stage of compressor at $290 \mathrm{~K}$, and every stage of turbine at $1200 \mathrm{~K}$. The thermal efficiency of this gas-turbine cycle is
(a) 36 percent
(b) 40 percent
(c) 52 percent
(d) 64 percent
(e) 76 percent

Key Concepts

Brayton Cycle

The Brayton cycle is the fundamental thermodynamic cycle used to describe the operation of gas turbines. It involves processes of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection. Understanding this cycle is essential for analyzing the performance and efficiency of gas turbine engines.

Regeneration in Gas Turbine Cycles

Regeneration involves using a heat exchanger (regenerator) to capture waste heat from the turbine exhaust and use it to preheat the compressed air before it enters the combustion chamber. This process reduces the amount of fuel required to reach the desired turbine inlet temperature, thereby improving the overall thermal efficiency of the cycle.

Pressure Ratio

The pressure ratio is the ratio of the compressor outlet pressure to the inlet pressure. It is a key parameter in gas turbine cycles because it directly influences the cycle’s thermal efficiency and work output. Higher pressure ratios typically enhance performance by increasing the cycle’s efficiency, though they also impose design challenges.

Thermal Efficiency

Thermal efficiency measures the effectiveness with which a gas turbine converts the energy from its fuel into useful work. It is influenced by the cycle’s temperature limits and the effectiveness of processes like regeneration. In ideal cycles, thermal efficiency is often determined by the temperature differences at various cycle points, and enhancements such as complete regeneration can significantly boost the efficiency.

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