Week 4. Gas Power Cycles IV
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
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 working fluid
http://www.youtube.com/watch?v=Srm7GcaL3DE&feature=related http://www.youtube.com/watch?v=cjjkj-UGboM
Stirling Engine
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)
Solar Dish/Stirling Power Systems
1) California Edison 25 kW dish/Stirling system 2) Advnco/Vanguard 25 kW dish/Stirling system installed at Rancho Mirage, California
3) 25 kW power conversion system under test at Sandia National Laboratories
1)
2)
3)
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
= −
= −
= = → =
2 in
1 3 out
4
1 4 2 3
2 3
1 4
th,Stirling
out th,Stirling
in
Supplied heat ln
Emitted heat ln
Process 2 3, 4 1 are isometric process ,
is
1 1
H
L
L H
q RT v
v q RT v
v
v v v v v v
v v
q T
q T
η
η
=
=
→ → = =
=
= − = −
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 back to the working fluid
A steady-flow Ericsson engine
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 3
th,Ericsson
in 1
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 H H
RT P
q P T
q RT P T
P T T Pv P v
v P v P
T T Pv P v v P
v P
η = − = − = −
→ = =
=
→ = =
=
Ex 4) Thermal Efficiency of the Ericsson Cycle
Using an ideal gas as the working fluid, show that the thermal efficiency of an Ericsson cycle is identical to the efficiency of a Carnot cycle operating between the same 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 engine
Summary
Brayton Cycle: Thermal Efficiency
T-s and P-v diagrams
for 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
≈ ≈
− + − = −
= − = −
= − = −
( )
( )
1 4
4 1 1
net out
th,Brayton
in in 3 2 3
2 2
2 3 4 1
2 2
1 1
The thermal efficiency of the ideal Brayton Cycle
1
1 1 1
1 Process 1-2 and 3-4 : isentropic process, and ,
p p
T T
c T T T
w q
q q c T T T T
T
P P P P
T P
T P
η
−
−
= = − = − = −
− −
= =
=
( ) ( )
( )
1 1
3 3
4 4
2
th,Brayton 1
1 p
Thus, 1- 1
where, r is the pressure ratio and is the specific heat ratio
k k k k
k k p p
P T
P T
r P r P
k η
− −
−
= =
= ⇐ =
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
Otto Cycle
Diesel Cycle
Brayton Cycle
Brayton Cycle: Thermal Efficiency II
Thermal efficiency of the ideal Brayton cycle as a function of the pressure ratio with K=1.4
• The thermal efficiency of an ideal Brayton cycle
depends on the pressure ratio of the gas turbine and the specific heat ratio of the working fluid.
(The thermal efficiency increases with both of these parameters.)
• In most common designs, the pressure ratio of gas turbines ranges from about 11 to 16
• Back work ratio: the ratio of the compressor work to the turbine work
• Development of Gas Turbines
1. Increasing the turbine inlet temperatures
540℃ → 1425℃ (new materials & innovative cooling techniques)
2. Increasing the efficiencies of turbo machinery components
3. Adding modifications to the basic cycle (e.g. intercooling regeneration and reheating)
( )
(
32 41)
4 3
1 2
T T c
T T
c h
h
h h
w bwr w
p p t
c
−
= −
−
= −
=
Ex 5) The Simple Ideal Brayton Cycle
A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 1300 K at the turbine inlet. Utilizing the air-standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine, (b) the back work ratio, and (c) the thermal efficiency.
Deviation of Actual Gas-Turbine Cycles from Idealized Ones
s a s
a T
a s a
s c
h h
h h
w w
h h
h h
w w
4 3
4 3
1 2
1 2
−
≅ −
=
−
≅ −
=
η η
The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities
• Some pressure drop during the heat-addition and heat rejection processes is inevitable
• The actual work input to the compressor is more
• The actual work output from the turbine is less because of irreversibilities
• The deviation can be accounted for by using the isentropic efficiencies of the turbine and compressor
