Thermodynamics for gas turbine cycles 1of2

Introduction to Thermodynamics for Gas
Turbine Cycles & Cycle Simulation Tools
A
Cycle
Innova-ons
Tutorial
Session

by
Pavlos
K.
Zachos
-‐
Luis
Sanchez
de
Leon
Department
of
Power
&
Propulsion
Cranﬁeld
University,
UK
ASME Turbo Expo 2013
San Antonio, US
1

CRANFIELD UNIVERSITY
DEPARTMENT OF POWER & PROPULSION
These slides have been prepared by Cranfield University for the
personal use of tutorial attendees. Accordingly, they may not be
communicated to a third party without the express permission of the
author(s). The slides are intended to support the tutorial in which they
are to be presented. However the content may be more comprehensive
than the presentations they are supporting.
Some of the data contained in the notes/slides may have been obtained
from public literature. However, in such cases, the corresponding
manufacturers or originators are in no way responsible for the accuracy
of such material.
All the information provided has been judged in good faith as appropriate
for the course. However, Cranfield University accepts no liability
resulting from the use of such information.
Disclaimer
2

Who we are...
Pavlos K. Zachos
Lecturer in Aerothermal Performance of Turbomachinery
Department of Power & Propulsion
Cranfield University, UK
p.zachos@cranfield.ac.uk
Luis Sanchez de Leon
Doctoral Researcher in Advanced Cycle Performance
Department of Power & Propulsion
Cranfield University, UK
l.sanchezdeleon@cranfield.ac.uk
Thermodynamics for Gas Turbine Cycles & Cycle Simulation Tools
ASME Turbo Expo San Antonio,Texas, 6th June 2013
3

PART I - Thermodynamics in our every day life.
4

PART II - A little bit of modelling.
5

PART III - A whole lot of modelling.
6

Why do you care ?
7

The science.
The people.
The product.
8

Thermo dynamics
θέρμη (therme)
heat
δυναμική
power
=
theory of relationship between heat and mechanical energy
Aeolipile (or Hero engine)
Hero of Alexandria
1st century AD
[source: Encyclopedia Britannica]
9

source: Wikipedia
10

1650
Otto von Guericke
invents the vacuum pump
1656
Boyle & Hooke
notice a correlation between
pressure, temperature and volume
18501750
1824
Carnot
correlates heat , power, energy & engine efficiency
Rankine - Clausius - Lord Kelvin
1st & 2nd Laws of Thermodynamics
1750
Savery
builds the first steam piston engine
to be later improved by Watt
Father of
Thermodynamics
equation of
state
11

Entropy, s
Temperature,T
1 2
34
Entropy, s
Temperature,T
1
2
3
4
Entropy, s
Temperature,T
1
2
3
4
v =
const.
v = const.
P = const.
v = const.
Entropy, s
Temperature,T
1
2
3
4
P =
const.
P = const.
Carnot cycle Ideal Otto cycle
Ideal Diesel cycle Ideal Brayton cycleThermodynamics for Gas Turbine Cycles & Cycle Simulation Tools
12

Why do you care ?
EAT.
BREATH.
TRAVEL.
14

Case study:
London to New York
5,526 km
100 days in 1866 by sailing ship
15 days in 1910 by early steam ships
3 days in 1960 by the fastest steam ship
< 8 hrs today by plane !!
15

= £475 per kg
[source: http://www.bullionbypost.co.uk on 21.5.2013]
=
Courtesy of Rolls-Royce
per kg
16

aerodynamics materials
fuels
emissions
mechanical
integrity
market research
&
logistics
system
integration
cycle
thermodynamics
controls
17

Entropy, s
Temperature,T
1
2
3
4
P =
const.
P = const.
George Brayton
1830 - 1892
Sir Frank Whittle
1907 - 1996
Dr Hans von Ohain
1911 - 1998
Courtesy of Rolls-Royce
18

Here’s to the crazy ones.
The misﬁts.
The rebels.
The troublemakers.
The ones who see things differently.
They are not fond of rules.
And they have no respect for the status quo.
You can praise them, disagree with them, quote,
disbelieve them, glorify or vilify them.
About the only thing you can’t do...
Apple advertising campaign
September 1997
19

...because they change things
21

...and also the way WE see things...
22

Let’s talk about today...
23

6 Trillion kg CO2
source: ClimateCrisis.netThermodynamics for Gas Turbine Cycles & Cycle Simulation Tools
24

20,000 kg
CO2 per year and person
4,500 kg
CO2 per year and person
25

450 ppm
29

10% less rainfall
30

Dust storm approaching Stratford,TEXAS - April 1935source: http://www.weru.ksu.edu
31

aerodynamics materials
fuels
emissions
mechanical
integrity
market research
&
logistics
system
integration
cycle
thermodynamics
controls
32

33

Families of thermodynamic cycles
Power
cycles
Refrigeration
cycles
Gas
cycles
Vapor
cycles
Closed
cycles
Open
cycles
35

Families of thermodynamic cycles
Power
cycles
Refrigeration
cycles
Gas
cycles
Vapor
cycles
Closed
cycles
Open
cycles
36

Basic considerations in the analysis of power cycles
1. Study the ideal cycle first
No friction
No heat losses
Quasi-equilibrium compressions & expansions
2. Neglect kinetic and potential energies
3. Use P-v or T-s diagrams
37

• Air as working fluid
• Ideal gas
Air standard assumptions
Equation of State: PV = RT
Cp
Cv
= γ R = Cp - Cv
• Semi-perfect gas
Cp / Cv functions of Temperature
γ= 1.33 - Turbines
γ= 1.40 - Compressors
38

Internal Energy
=
The total energy contained by a thermodynamic system
39

Internal Energy = u(T)
40

u(T) + pV = Enthalpy
41

u(T) + pV = Enthalpy
u(T) + RT = Enthalpy = h(T)
42

Speciﬁc Heat Capacity at ConstantVolume
43

=
Cv
44

=
Cv =
du
dT
45

Speciﬁc Heat Capacity at Constant Pressure
46

=
Cp
47

=
Cp =
dh
dT
48

Ideal Gas Model
PV = RT
Internal Energy = u(T) = Cv T
Enthalpy = u(T) + RT = h(T) = Cp T
Cp
Cv
=γ
γ= 1.33 - Turbines
γ= 1.40 - Compressors
49

Wilcock R. C.,Young J. B., and Horlock J. H., 2002,“Gas properties as
a limit to gas turbine performance.”
Kyprianidis K., SethiV., Ogaji S. O., PILIDIS P., Singh R., and KALFAS A. I., 2009,
“Thermo-Fluid Modelling for Gas Turbines-Part I:Theoretical Foundation and
Uncertainty Analysis.”
Kyprianidis K., SethiV., Ogaji S. O., PILIDIS P., Singh R., and KALFAS A. I., 2009,
“Thermo-Fluid Modelling for Gas Turbines-Part II: Impact on Performance
Calculations and Emissions Predictions at Aircraft System Level.”
50

Entropy, s
Temperature,T
1
2
3
4
P2 =
const.
P1 = const.
heat in
heat out
work
in
maximum cycle pressure
limited by compressor
technology
maximum cycletemperaturelimited by turbinetechnology
work out
Useful
work
(Net)
51

Entropy, s
Temperature,T
1
2
3
4
P2 =
const.
P1 = const.
heat in
heat out
work
in
work
out
Compressor Turbine
Combustion
chamber
Ideal Brayton cycle processes:
1-2: Isentropic compression
2-3: Constant pressure heat addition
3-4: Isentropic expansion
4-1: Constant pressure heat rejection
52

53

win
54

win
qin
+
55

win
qin
+
wout
-
56

win
qin
+
wout
-
qout
-
Inlet
Enthalpy
Outlet
Enthalpy
(qin - qout) + (win - wout) = 0
= -wnet
wnet = qin - qout
Steady-ﬂow process energy balance on a unit-mass basis:
-=
57

wnet = qin - qout
qin = h3 - h2 = cp (T3 - T2)
qout = h4 - h1 = cp (T4 - T1)
58

Entropy, s
Temperature,T
1
2
3
4
P2 =
const.
P1 = const.
heat in
heat out
work
in
work
out
Compressor Turbine
Combustion
chamber
Fresh
air
Fuel
Exhaust
gases
work out
wnet = qin - qout
qin = h3 - h2 = cp (T3 - T2)
qout = h4 - h1 = cp (T4 - T1)
ηthermal =
wnet
qin
= 1-
qout
qin
using...
T2
T1
=
P2
P1
( )
γ-1/γ
=
P3
P4
( )
γ-1/γ
=
T3
T4
ηthermal = 1-
1
P2
P1
γ-1/γ
59

Entropy, s
Temperature,T
1
2
3
4
P2 =
const.
P1 = const.
heat in
heat out
work
in
work
out
Compressor Turbine
Combustion
chamber
Fresh
air
Fuel
Exhaust
gases
work out
ηthermal = 1-
1
P2
P1
γ-1/γ
ηthermal Pressure ratio
Is this right ?
60

Entropy, s
Temperature,T
1
2s
4s2a
in reality...
- no compression/expansion is
isentropic &
- some pressure loss is inevitable
4a
3
ηcompr
ηturb
=
=
h2s - h1
h2a - h1
h3 - h4a
h3 - h4s
Component isentropic
efficiencies:
note
for preliminary cycle
modelling component
efficiencies can be guessed
or estimated
61

Case
study
#1:
Eﬀect
of
compressor
eﬃciency
on
cycle
performance
Compressor Turbine
Combustion
chamber
- Standard air assumptions
- Standard ISA conditions:
288.15K @ 1 bar
- Constant ηt,is
- T3 = 1600K
- Combustion efficiency=0.98
- Account for cooling flows
isentropic
Isentropic
0.9
0.85
0.8
62

0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1 3 5 7 9 11 13 15
OVERALL PRESSURE RATIO
ISENTROPICEFFICIENCY
POLYTROPIC EFFICIENCY = 0.90
0.85
0.8
63

Case
study
#2:
Eﬀect
of
Turbine
Entry
Temperature
on
cycle
performance
Compressor Turbine
Combustion
chamber
- Standard air assumptions
- Standard ISA conditions:
288.15K @ 1 bar
- Constant ηt,is
- Combustion efficiency=0.98
- Account for cooling flows
Assuming a value for the polytropic efficiency of
our compressor a new isentropic efficiency is
calculated for every pressure ratio based on:
TET = 1000 K
1200 K
1400 K
1600 K 1800 K
64

Cycle
design
in
a
gas
turbine
performance
solver
Use
of
“BRICKS”
Compressor Turbine
Combustion
chamber
Thrust
per unit flow
Intake
Fresh
air
ALTITUDE
MACH No.
Rel. Humidity
PRESSURE
RECOVERY
FACTOR
PRESSURE
RATIO
POLYTROPIC
EFFICIENCY
BLEED FLOWS
COMBUSTION
EFFICIENCY
PRESSURE
LOSS
TURBINE ENTRY
TEMPERATURE
(TET)
ISENTROPIC
EFFICIENCY
COOLING
FLOWS
Nozzle
65

Cycle
design
in
a
gas
turbine
performance
solver
Use
of
“BRICKS”
Compressor Turbine
Combustion
chamber
Intake
Fresh
air
ALTITUDE
MACH No.
Rel. Humidity
PRESSURE
RECOVERY
FACTOR
PRESSURE
RATIO
POLYTROPIC
EFFICIENCY
BLEED FLOWS
COMBUSTION
EFFICIENCY
PRESSURE
LOSS
TURBINE ENTRY
TEMPERATURE
(TET)
ISENTROPIC
EFFICIENCY
COOLING
FLOWS
Output Power
per unit flow
66

Case
study
#3:
Single
spool
gas
generator
design
space
exploraIon
Compressor Turbine
Combustion
chamber
Intake
Fresh
air
ALTITUDE
MACH No.
Rel. Humidity
PRESSURE
RECOVERY
FACTOR
PRESSURE
RATIO
POLYTROPIC
EFFICIENCY
BLEED FLOWS
COMBUSTION
EFFICIENCY
PRESSURE
LOSS
TURBINE ENTRY
TEMPERATURE
(TET)
ISENTROPIC
EFFICIENCY
COOLING
FLOWS
Output Power
per unit flow
0.9
0.98
5%
0.91
Specific
Fuel
Consumption
=
Fuel ﬂow [kg/s]
definitions
or SFC
Specific
Power
=
Net Output [J/s]
Net Output [J/s]
Mass ﬂow [kg/s]
67

PR = 3
PR = 6
PR = 15TET = 1000 K
TET = 1200 K
TET = 1400 K
TET = 1600 K
Large size
High weight
Small size
Low weight
Low
technology
High
technology
68

Compressor Turbine
Combustion
chamber
Intake
Fresh
air
ALTITUDE
MACH No.
Rel. Humidity
PRESSURE
RECOVERY
FACTOR
PRESSURE
RATIO
POLYTROPIC
EFFICIENCY
BLEED FLOWS
COMBUSTION
EFFICIENCY
PRESSURE
LOSS
TURBINE ENTRY
TEMPERATURE
(TET)
ISENTROPIC
EFFICIENCY
COOLING
FLOWS
Thrust
per unit flow
Nozzle
69

High
Pressure
Compressor
Combustion
chamber
Low
Pressure
Compressor
Low
Pressure
Turbine
High
Pressure
Turbine
COMING UP NEXT...
70

High
Pressure
Compressor
Combustion
chamber
Low
Pressure
Compressor
Low
Pressure
Turbine
High
Pressure
Turbine
COMING UP NEXT...
71

High
Pressure
Compressor
Combustion
chamber
Low
Pressure
Compressor
Low
Pressure
Turbine
High
Pressure
Turbine
COMING UP NEXT...
72

High
Pressure
Compressor
Combustion
chamber
Low
Pressure
Compressor
Low
Pressure
Turbine
High
Pressure
Turbine
Combustion
chamber
COMING UP NEXT...
73

High
Pressure
Compressor
Combustion
chamber
Low
Pressure
Compressor
Low
Pressure
Turbine
High
Pressure
Turbine
Combustion
chamber
COMING UP NEXT...
74

Related textbooks
75

Related textbooks
76

Introduction to Thermodynamics for Gas
Turbine Cycles & Cycle Simulation Tools
further
info,
compliments
&
complaints
to
be
addressed
to:
p.zachos@cranﬁeld.ac.uk

ASME Turbo Expo 2013
San Antonio, US
77

Thermodynamics for gas turbine cycles 1of2

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