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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