Chapter 9Chapter 9GAS POWER CYCLES

(Part II)(Part II)

Brayton Cycle: Ideal Cycle for Gas-Turbine EnginesGas turbines usually operate on an open cycle (Fig. 9–29). Air at ambient conditions is drawn into the compressor, where its temperature and pressure are raised The high pressure air proceeds into the combustion chamber pressure are raised. The high pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure.

The high-temperature gases then The high temperature gases then enter the turbine where they expand to atmospheric pressure while producing power output. p g p pSome of the output power is used to drive the compressor.The exhaust gases leaving the The exhaust gases leaving the turbine are thrown out (not re-circulated), causing the cycle to be classified as an open cycle.

2p y

Closed Cycle ModelThe open gas-turbine cycle can be modelled as a closed cycle, using

Closed Cycle Model

the air-standard assumptions (Fig. 9–30). The compression and expansion processes remain the same, but the combustion process is replaced by a constant-pressure heat addition process from an external source. The exhaust process is replaced by a constant-pressure heat rejection process to the ambient air.

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The Brayton CycleThe ideal cycle that the working fluid undergoes in the closed loop is the Brayton cycle. It is made up of four internally

ibl reversible processes:1-2 Isentropic compression;2-3 Constant-pressure heat addition;3-4 Isentropic expansion;4-1 Constant-pressure heat rejection.

The T-s and P-v diagrams of an ideal Brayton cycle are shown in Fig. 9–31.Note: All four processes of the Brayton cycle are executed in steady-flow devices thus, they should be analyzed as steady-flow processes.

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Thermal EfficiencyThe energy balance for a steady-flow process can be expressed, on a unit–mass basis, as

The heat transfers to and from the working fluid are:

The thermal efficiency of the ideal Brayton cycle,

Constant specific heats

5is the pressure ratio.where

Parameters Affecting Thermal Efficiencyg y

The thermal efficiency of an ideal Brayton cycle depends on the pressure ratio, rp of the gas turbine and the specific heat ratio, k of the working fluid.

The thermal efficiency increases with both of these parameters, which is also the case for actual gas turbines.

6A plot of thermal efficiency versus the pressure ratio is shown in Fig. 9–32, for the case of k =1.4.

Improvements of Gas Turbine’s PerformanceThe early gas turbines (1940s to 1959s) found only limited use despite theirversatility and their ability to burn a variety of fuels, because its thermal efficiencywas only about 17%. Efforts to improve the cycle efficiency are concentrated inthree areas:

1. Increasing the turbine inlet (or firing) temperatures.The turbine inlet temperatures have increased steadily from about 540°CThe turbine inlet temperatures have increased steadily from about 540 C(1000°F) in the 1940s to 1425°C (2600°F) and even higher today.

2. Increasing the efficiencies of turbo-machinery components (turbines,compressors).p )The advent of computers and advanced techniques for computer-aided designmade it possible to design these components aerodynamically with minimallosses.

3. Adding modifications to the basic cycle (intercooling, regeneration orrecuperation, and reheating).The simple-cycle efficiencies of early gas turbines were practically doubled byincorporating intercooling, regeneration (or recuperation), and reheating.

7incorporating intercooling, regeneration (or recuperation), and reheating.

Actual Gas-Turbine CyclesSome pressure drop occurs during the heat-addition and heat rejection processes. The actual work input to the compressor is more, and the actual work output from the turbine is less, because of irreversibilities.

D i ti f t l dDeviation of actual compressor andturbine behavior from the idealizedisentropic behavior can be accountedfor by utilizing isentropic efficienciesfor by utilizing isentropic efficienciesof the turbine and compressor.

Turbine:

Compressor: 8Compressor:

Brayton Cycle With RegenerationTemperature of the exhaust gas leaving the turbine is higher than the temperature of the air leaving the compressor. The air leaving the compressor can be heated by the The air leaving the compressor can be heated by the hot exhaust gases in a counter-flow heat exchanger (a regenerator or recuperator) – a process called regeneration (Fig. 9-38 & Fig. 9-39). The thermal efficiency of the Brayton cycle increases due to regeneration since less fuel is used for the same work output.

Note: The use of a regenerator The use of a regenerator is recommended only when the turbine exhaust temperature is higher than the compressor exit 9the compressor exit temperature.

Effectiveness of the RegeneratorAssuming the regenerator is well insulated and changes in kinetic and potential energies are negligible, the actual and maximum heat transfers from the exhaust gases to the air can be expressed as

Effectiveness of the regenerator,

Effectiveness under cold-air standard assumptions,

Thermal efficiency under cold-air 10standard assumptions,

Factors Affecting Thermal

Thermal efficiency of Brayton cycle

Factors Affecting Thermal Efficiency

y y ywith regeneration depends on:

a) ratio of the minimum to maximum temperatures, and

b) the pressure ratio. Regeneration is most effective at lower pressure ratios and smallminimum-to-maximum temperature ratios.

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Brayton Cycle With Intercooling, Reheating & RegenerationReheating, & RegenerationThe net work output of a gas-turbine cycle can be increased by either:can be increased by either:

a) decreasing the compressor work, or b) increasing the turbine work, orc) both.c) both.

The compressor work input can be decreased bycarrying out the compression process in stages

d li th i b t (Fi 9 42) iand cooling the gas in between (Fig. 9-42), usingmultistage compression with intercooling.

The work output of a turbine can be increased byThe work output of a turbine can be increased byexpanding the gas in stages and reheating it inbetween, utilizing a multistage expansion withreheating.

12g

Physical arrangement of an ideal two-stage gas-turbine cycle with intercooling reheating andturbine cycle with intercooling, reheating, andregeneration is shown in Fig. 9-43.

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Conditions for Best PerformanceThe work input to a two-stage compressor is minimized when equal pressureratios are maintained across each stage. This procedure also maximizes theturbine work output.Thus, for best performance we have,

Intercooling and reheating alwaysdecreases thermal efficiency unlessare accompanied by regeneration.Therefore, in gas turbine powerplants, intercooling and reheating arealways used in conjunction withregeneration.

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SKIP THE FOLLOWING SLIDES…!

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Second-law Analysis of Gas Power CyclesTh id l Ott Di l d B t l i l i ibiliti t l tThe ideal Otto, Diesel, and Brayton cycles may involve irreversibilities external tothe system. A second-law analysis of these cycles will reveal where the largestirreversibilities occur and where to start the improvements.

The exergy destruction for a closed system can be expressed as

Exergy

A i il l ti f t d fl t

Exergy Destruction!

A similar relation for steady-flow systems can be expressed, in rate form, as

On a unit–mass basis, for a one-inlet, one-exit steady-flow device,

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The exergy destruction of a cycle isth f th d t tithe sum of the exergy destructionsof the processes that compose thatcycle.It d d th it d f thIt depends on the magnitude of theheat transfer with the high- and low-temperature reservoirs involvedand on their temperatures For a cycle that involves heat transfer and on their temperatures. only with a source at TH and a sink at

TL, the exergy destruction becomes

Cl d t

Exergy of …Closed system,

Flow stream,17