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The main parameters of ideal and real Brayton cycles are the turbine-inlet temperature, T3, the compressor pressure ratio, =p2/p1 (within the range 4..40), the compressor and turbine efficiencies, and the size, measured by the air mass flow rate. The energy and exergy efficiencies for the ideal Brayton cycle (compressor and turbine efficiencies of 100%), can be expressed as: net 1 W1T11 and 2 W1 T (17.5) e,Brayton Q T 1 W 1 T T3 max 1 x,Brayton pos2 max1 Real engine efficiencies are comparatively low, from 25% to 40% (it was only 15% when they started, in the 1950s), but in combination with a bottoming vapour cycle, they reach 50..59% based on LHV; combined cycle power plants are the present standard in electricity generation. Contrary to reciprocating and steam engines, the gas turbine can only work with fine-tuned components, since it gives no net power if the compressor and turbine efficiencies fall below say 80% (modern gas turbines can have compressor efficiencies of 80% to 88%, and turbine efficiencies of 88% to 90%). The two factors that most affect gas-turbine efficiency are turbine-inlet temperature and pressure ratio, which should be the highest the possible. Turbine-inlet temperature has increased almost linearly from 1100 K in the 1950s to 1800 K in modern aircraft gas turbines with blade cooling. Pressure ratio has also increased almost linearly from 10:1 in the 1950s to 40:1 in modern aircraft gas turbines. It is easy to prove that for fixed extreme temperatures (ambient and turbine-inlet) there is a pressure ratio that maximises the work per unit mass flow rate, thus rendering the smallest engine for a given power, this optimum value being: T321 where C and T are the compressor and turbine isentropic efficiencies, defined in Chapter 5 (5.28-29). Several improvements to the simple Brayton cycle are in use. Besides the multistage compression and expansion explained in Chapter 5, the main variant is the regenerative cycle (Fig. 17.6), where heat from the exhaust gasses is used (from point 4 to 5) to heat up air before entering the combustion chamber (from point 2 to ideally up to point 2' in Fug. 17.6, although in practice the heat exchanger efficiency will limit this value). The heat recovery from the exhaust gasses may be also performed externally to the cycle, e.g. generating vapour in a heat exchanger (boiler), that may be directly used for heating applications or may even get expanded in a vapour turbine to produce further work (combined Brayton and Rankine cycles). Example 3. A Brayton cycle engine Other gas cycles Practical gas engines are basically internal-combustion engines, either piston engines, or gas turbines. Their thermodynamic processes are best represented by the dual cycle and the Brayton cycle, respectively. But there are other gas cycles of interest in power generation, like the Stirling cycle, which is actually the first gas-cycle ever proposed, invented in 1816 by the Scottish clergyman Robert Stirling, the Atkinson cycle (patented in 1877 by Atkinson as a modification of the Otto cycle), and so on. The Stirling engine is an external heat-input engine (can be driven by external combustion, solar w CTT (17.6) 1 1 TPDF Image | THERMAL MACHINES AND HEAT ENGINES
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