Week 5. Gas Power CyclesV

Week 5. Gas Power Cycles V

Objectives

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

2. Develop simplifying assumptions applicable to gas power cycles 3. Discuss both approximate and exact analysis of gas power cycles 4. Review the operation of reciprocating engines

5. Solve problems based on the Otto, Diesel, Stirling, and Ericsson cycles 6. Solve problems based on the Brayton cycle; the Brayton cycle with

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

7. Analyze jet-propulsion cycles

8. Identify simplifying assumptions for second-law analysis of gas power cycles

9. Perform second-law analysis of gas power cycles

The Brayton Cycle With Regeneration

A gas-turbine engine with regenerator

• In gas-turbine engines, the temperature of the exhaust gas leaving the turbine is often

considerably higher than the

temperature of the air leaving the compressor

• Regenerator (=recuperator): The high-pressure air leaving the

compressor can be heated by

transferring heat to it from the hot exhaust gases in a counter flow heat exchanger

1 → 2 : Adiabatic compression by compressor

2 → 5 : Absorbing generated heat (q_reg) by regenerator 5 → 3 : Combustion (q_in)

3 → 4 : Adiabatic expansion by turbine

4 → 6 : Releasing waste heat (q_reg) from exhaust gas 6 →1 : Heat release (q_out)

The Brayton Cycle With Regeneration II

T-s diagram of a Brayton cycle with regeneration

2 4

2 5

regen.max

2 5

regen.act

h h

h h

q

h h

q

−

=

−

=

−

=

′

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

Effectiveness (ε): the extent to which a

regenerator approaches an ideal regenerator

2 4

2 5

max regen,

act regen,

h h

h h

q q

−

= − ε =

2 4

2 5

T T

T T

−

≅ − ε

Under the cold-air-standard assumptions

The Brayton Cycle With Regeneration III

Thermal efficiency of the ideal Brayton cycle with and without regeneration

• A generator with a higher effectiveness obviously saves a greater amount of fuel since 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 of an ideal Brayton cycle with regeneration is

• This figure shows that regeneration is most effective at lower pressure ratios and

low minimum-to-maximum temperature ratios

( ) ^r

T

T

3 1 regen

th,

1  

 



− 

η =

Ex 7) Actual Gas-Turbine Cycle with Regeneration

Determine the thermal efficiency of the gas- turbine described in Ex 6 if a regenerator having an effectiveness of 80 percent is installed.

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

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

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 inlet

temperature, 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 specific volume of the fluid. Therefore, the specific volume of the working fluid should be as low as possible during a compression process and as high as possible during an expansion process

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

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

T-s diagram of an ideal gas-turbine cycle with intercooling, reheating, and regeneration

( ) ( )

( ) ( )

( ) ( )

out th,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

= −

= + = − + −

= + = − + −

= = = → =

= −

= −

− + − −

=

( ) ( )

(

) (

)

h h h h

h h h h

− − −

− + −

The Brayton Cycle with Inter-cooling, Reheating And Regeneration

As the number of compression and expansion stages increases, the gas turbine cycle with intercooling,

reheating, and regeneration approaches the Ericsson cycle

• Intercooling and reheating always decreases the thermal efficiency unless they are accompanied by regeneration. This is because intercooling decreases the average temperature at which heat is added, and reheating increases the average temperature at 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 Ericsson cycle and the thermal efficiency approaches the theoretical limit (the Carnot efficiency)

• 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

Ex 8) A Gas Turbine with Reheating and Intercooling

An ideal gas-turbine cycle with two stages of compression and two stages of expansion has an overall pressure ratio of 8. Air enters each stage of the compressor at 300 K and each stage of the turbine at 1300 K. Determine the back work ratio and the thermal efficiency of this gas-turbine cycle, assuming (a) no regenerators and (b) an ideal regenerator with 100 percent effectiveness. Compare the results with those obtained 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 of specific heat or the constant specific heat (Cold-air-standard assumption)

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

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