Week 4. Gas Power Cycles IV

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

Stirling And Ericsson Cycles II

Stirling Cycle proposed by Robert Stirling in 1828

• Process 1→2 : isothermal expansion : heat addition

from external source

• Process 2→3 : constant volume regeneration : internal

heat transfer from the working fluid to the regenerator

• Process 3→4 : isothermal compression : heat rejection to the external sink• Process 4→1 : constant volume regeneration : internal heat transfer from the regenerator back to the workingfluid

http://www.youtube.com/watch?v=Srm7GcaL3DE&feature=relatedhttp://www.youtube.com/watch?v=cjjkj-UGboMhttp://www.youtube.com/watch?v=1RNNlYiKxlc&NR=1http://www.youtube.com/watch?v=7Q4UENGN_Ykhttp://www.youtube.com/watch?v=fUrB7KRvxUk&feature=fvw

Stirling Engine

GENESYS Laboratory

1. How a Stirling engine works

2. Laminar Flow Stirling Engine

3. The Stirling Motor

4. Solar powered Stirling Engine with Fresnel Lens

Stirling And Ericsson Cycles I

• Stirling Engine (Video Clips)

GENESYS Laboratory

Solar Dish/Stirling Power Systems

1) California Edison 25 kW dish/Stirling system

2) Advnco/Vanguard 25 kW dish/Stirling systeminstalled at Rancho Mirage, California

3) 25 kW power conversion system under testat Sandia National Laboratories

1)

2)

3)

GENESYS Laboratory

Stirling And Ericsson Cycles III

Thermal efficiency of Stirling cycle

41 1 4

23 2 3

1 2 4 3 41 23

( )

( )

,

v

v

q c T T

q c T T

T T T T q q

= −

= −

= = → =

2in

1

3out

4

1 4 2 3

32

1 4

th,Stirling

outth,Stirling

in

Supplied heat ln

Emitted heat ln

Process 2 3, 4 1 are isometric process ,

is

1 1

H

L

L

H

vq RT

v

vq RT

v

v v v v

vv

v v

q T

q T

η

η

=

=

→ → = =

=

= − = −

GENESYS Laboratory

Stirling And Ericsson Cycles IV

The Ericsson cycle is very much like the

Stirling cycle, except that the two constant-

volume processes are replaced by two

constant-pressure processes

Process 1→2 : isothermal expansion : heat

addition from external source

Process 2→3 : constant pressure regeneration :

internal heat transfer from the working fluid to

the regenerator

Process 3→4 : isothermal compression : heat

rejection to the external sink

Process 4→1 : constant pressure regeneration : internal heat transfer from the regenerator backto the working fluid

A steady-flow Ericsson engine

GENESYS Laboratory

Stirling And Ericsson Cycles V

Thermal efficiency of Ericson cycle

41 1 4

23 2 3

1 2 4 3 41 23

( )

( )

,

P

P

q c T T

q c T T

T T T T q q

= −

= −

= = → =

4

out 3th,Ericsson

1in

2

1 2 1 1 2 2

1 2

2 1

3 4 3 3 4 4

3 4

4 3

ln

1 1 1

ln

Process 1 2; ,

Process 3 4; ,

L

L

HH

PRT

q P T

Pq TRTP

T T Pv Pv

v P

v P

T T Pv Pv

v P

v P

η = − = − = −

→ = =

=

→ = =

=

GENESYS Laboratory

Ex 4) Thermal Efficiency of the Ericsson Cycle

GENESYS Laboratory

Using an ideal gas as the working fluid, show that the thermal efficiency of anEricsson cycle is identical to the efficiency of a Carnot cycle operating between thesame temperature limits.

Brayton Cycle: The ideal Cycle for Gas-Turbine Engines

• Proposed by George Brayton in 1870s

• It is an open cycle, but it can be modeled as a

closed cycle by utilizing the air-standard

assumptions

• The two major application areas of gas-

turbine engines are aircraft propulsion and

electric power generation

• It is made up of four internally reversible

processes:

Process 1→2 : Isentropic compression (in a

compressor)

Process 2→3 : Constant pressure heat

addition

Process 3→4 : Isentropic expansion (in a

turbine)

Process 4→1 : Constant-pressure heat rejection

An open-cycle gas-turbine engine

A closed-cycle gas-turbine engineGENESYS Laboratory

Summary

GENESYS Laboratory

Brayton Cycle: Thermal Efficiency

T-s and P-v diagramsfor the ideal Brayton cycle

( ) ( )

( )

( )

in out in out exit inlet

in 3 2 3 2

out 4 1 4 1

The energy balance for a steady-flow process, when 0

heat transfers to and from the working fluid are

p

p

ke pe

q q w w h h

q h h c T T

q h h c T T

≈ ≈

− + − = −

= − = −

= − = −

( )( )

41

4 1 1net outth,Brayton

3in in 3 22

2

2 3 4 1

2 2

1 1

The thermal efficiency of the ideal Brayton Cycle

11 1 1

1

Process 1-2 and 3-4 : isentropic process, and ,

p

p

TTc T T Tw q

Tq q c T T TT

P P P P

T P

T P

η

− − = = − = − = −− −

= =

=

( ) ( )

( )

1 1

3 3

4 4

2th,Brayton 1

1

p

1Thus, 1-

where, r is the pressure ratio and is the specific heat ratio

k k k k

pk k

p

P T

P T

Pr

Pr

k

η

− −

−

= =

= ⇐ =

GENESYS Laboratory

Summary

Process 1→2 : isentropic compression

Process 2→3 : constant volume heat addition

Process 3→4 : isentropic expansion

Process 4→1 : constant volume heat rejection

Process 1→2 : isentropic compression

Process 2→3 : constant pressure heat addition

Process 3→4 : isentropic expansion

Process 4→1 : constant volume heat rejection

Process 1→2 : isentropic compression

Process 2→3 : constant pressure heat addition

Process 3→4 : isentropic expansion

Process 4→1 : constant pressure heat rejection

Otto Cycle

Diesel Cycle

Brayton Cycle

GENESYS Laboratory

Brayton Cycle: Thermal Efficiency II

Thermal efficiency of the idealBrayton cycle as a function ofthe pressure ratio with K=1.4

• The thermal efficiency of an ideal Brayton cycledepends on the pressure ratio of the gas turbine and thespecific heat ratio of the working fluid.(The thermal efficiency increases with both of these

parameters.)• In most common designs, the pressure ratio of gasturbines ranges from about 11 to 16• Back work ratio: the ratio of the compressor work to theturbine work

• Development of Gas Turbines1. Increasing the turbine inlet temperatures

540℃→ 1425℃ (new materials & innovative coolingtechniques)

2. Increasing the efficiencies of turbo machinerycomponents

3. Adding modifications to the basic cycle (e.g. intercoolingregeneration and reheating)

( )( )43

12

43

12

TTc

TTc

hh

hh

w

wbwr

p

p

t

c

−

−=

−

−==

GENESYS LaboratoryGas Turbine

Ex 5) The Simple Ideal Brayton Cycle

GENESYS Laboratory

A gas-turbine power plant operating on an idealBrayton cycle has a pressure ratio of 8. The gastemperature is 300 K at the compressor inlet and 1300K at the turbine inlet. Utilizing the air-standardassumptions, determine (a) the gas temperature at theexits of the compressor and the turbine, (b) the backwork ratio, and (c) the thermal efficiency.

Deviation of Actual Gas-Turbine Cyclesfrom Idealized Ones

s

a

s

aT

a

s

a

sc

hh

hh

w

w

hh

hh

w

w

43

43

12

12

−

−≅=

−

−≅=

η

η

The deviation of an actual gas-turbinecycle from the ideal Brayton cycle as aresult of irreversibilities

• Some pressure drop during the heat-additionand heat rejection processes is inevitable• The actual work input to the compressor ismore• The actual work output from the turbine is lessbecause of irreversibilities• The deviation can be accounted for by usingthe isentropic efficiencies of the turbine andcompressor

GENESYS Laboratory