Week 5. Gas Power Cycles V

GENESYS Laboratory

Objectives

1. Evaluate the performance of gas power cycles for which the workingfluid remains a gas throughout the entire cycle

2. Develop simplifying assumptions applicable to gas power cycles3. Discuss both approximate and exact analysis of gas power cycles4. Review the operation of reciprocating engines5. Solve problems based on the Otto, Diesel, Stirling, and Ericsson cycles6. Solve problems based on the Brayton cycle; the Brayton cycle with

regeneration; and the Brayton cycle with intercooling, reheating, andregeneration

7. Analyze jet-propulsion cycles8. Identify simplifying assumptions for second-law analysis of gas power

cycles9. Perform second-law analysis of gas power cycles

GENESYS Laboratory

The Brayton Cycle With Regeneration

A gas-turbine engine with regenerator

• In gas-turbine engines, thetemperature of the exhaust gasleaving the turbine is oftenconsiderably higher than thetemperature of the air leaving thecompressor• Regenerator (=recuperator): Thehigh-pressure air leaving thecompressor can be heated bytransferring heat to it from the hotexhaust gases in a counter flow heatexchanger

1 → 2 : Adiabatic compression by compressor

2 → 5 : Absorbing generated heat (qreg) by regenerator

5 → 3 : Combustion (qin)

3 → 4 : Adiabatic expansion by turbine

4 → 6 : Releasing waste heat (qreg) from exhaust gas

6 →1 : Heat release (qout)GENESYS Laboratory

The Brayton Cycle With Regeneration II

T-s diagram of a Brayton cycle withregeneration

2425regen.max

25regen.act

hhhhq

hhq

−=−=

−=

′

The actual and maximum heat transfers from the exhaust gases to the air

Effectiveness (ε): the extent to which aregenerator approaches an ideal regenerator

24

25

maxregen,

actregen,

hh

hh

q

q

−

−==ε

24

25

TT

TT

−

−≅ε

Under the cold-air-standard assumptions

GENESYS Laboratory

The Brayton Cycle With Regeneration III

Thermal efficiency of the ideal Braytoncycle with and without regeneration

• A generator with a higher effectiveness obviously saves a greater amount of fuelsince it preheats the air to a higher temperature prior to combustion• The effectiveness of most regenerators used in practice is below 0.85• Under the cold-air-standard assumptions, the thermal efficiency ofan ideal Brayton cycle with regeneration is

• This figure shows that regeneration is mosteffective at lower pressure ratios andlow minimum-to-maximum temperature ratios

( )( ) kk

prT

T 1

3

1regenth, 1

−

−=η

GENESYS Laboratory

Ex 7) Actual Gas-Turbine Cycle with Regeneration

GENESYS Laboratory

Determine the thermal efficiency of the gas-turbine described in Ex 6 if a regeneratorhaving an effectiveness of 80 percent isinstalled.

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

A gas-turbine engine with two-stage compression with inter-cooling, two-stage expansion withreheating, and regeneration

GENESYS Laboratory

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

• Multistage compression with inter-cooling: As the number of stages is increased,the compression process becomes nearly isothermal at the compressor inlettemperature, and the compression work decreases• Multistage expansion with reheating: As the number of stages is increased,the expansion process becomes nearly isothermal• The steady-flow compression or expansion work is proportional to the specificvolume of the fluid. Therefore, the specific volume of the working fluid should beas low as possible during a compression process and as high as possible duringan expansion process

Comparison of work inputs to a single-stage compressor and a two-stagecompressor with intercooling

GENESYS Laboratory

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

T-s diagram of an ideal gas-turbinecycle with intercooling, reheating, andregeneration

( ) ( )

( ) ( )

( ) ( )

outth,reh-reg

in

in in,comb in,reh 6 5 8 7

out out,exh out,ic 10 1 2 3

9 5 10 4 1 3 1 3

th,reh-reg

in

6 7 8 9

1

for ideal case : , and if

and t c

t c

q

q

q q q h h h h

q q q h h h h

h h h h T T h h

w w w

w w

q

h h h h

η

η

= −

= + = − + −

= + = − + −

= = = → =

= −

−=

− + − −=

( ) ( )( ) ( )

2 1 4 3

6 5 8 7

h h h h

h h h h

− − −

− + −

GENESYS Laboratory

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

As the number of compression andexpansion stages increases, the gasturbine cycle with intercooling,reheating, and regeneration approachesthe Ericsson cycle

• Intercooling and reheating always decreases the thermal efficiency unless they areaccompanied by regeneration. This is because intercooling decreases the averagetemperature at which heat is added, and reheating increases the average temperatureat which heat is rejected.• If the number of compression and expansion stages is increased, the ideal gas-turbine cycle with intercooling, reheating, and regeneration approaches the Ericssoncycle and the thermal efficiency approaches the theoretical limit (the Carnotefficiency)• The contribution of each additional stage to the thermal efficiency is less and less,and the use of more than two or three stages cannot be justified economically

GENESYS Laboratory

Ex 8) A Gas Turbine with Reheating and Intercooling

GENESYS Laboratory

An ideal gas-turbine cycle with two stages ofcompression and two stages of expansion has anoverall pressure ratio of 8. Air enters each stage of thecompressor at 300 K and each stage of the turbine at1300 K. Determine the back work ratio and the thermalefficiency of this gas-turbine cycle, assuming (a) noregenerators and (b) an ideal regenerator with 100percent effectiveness. Compare the results with thoseobtained in Ex 5.

Summary

Here is a tip!

1) Note the type of cycle (e.g. Otto, Diesel, Brayton, Rankine, etc)

2) Draw P-v and T-s diagram

3) Assumption is important, which is either the variation ofspecific heat or the constant specific heat (Cold-air-standardassumption)

4) For the variation of specific heat, use relative propertieswith Table A-17

5) For the constant specific heat, use isentropic correlations.

GENESYS Laboratory