applications of gas turbine engines review of ...scp/scp/ocw/aerospace... · •recap: lecture 2:...
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• Recap: Lecture 2: 24th July 2015, 1530-1655 hrs.
– Applications of gas turbine engines
– Review of thermodynamics concepts
• Energy, Enthalpy, Entropy
• T-s diagram
• Isentropic processes
• Tds equations
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Energy analysis of steady flow systems
• For single entry and exit devices,
)(2
mass,unit per or
)(2
12
2
1
2
212
12
2
1
2
212
zzgVV
hhwq
zzgVV
hhmWQ
2
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Turbines and compressors
Turbine
WT
1
2
Control surface
Insulation
m
m
3
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Turbines and compressors
• For a turbine for eg., the energy equation would be:
)(
,negligible are PE and KE If
)2
()2
(
21
2
2
221
2
11
hhmW
gzV
hmWgzV
hm
out
out
4
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Stagnation properties
• Enthalpy represents the total energy of a fluid in the absence of potential and kinetic energies.
• For high speed flows, though potential energy may be negligible, but not kinetic energy.
• Combination of enthalpy and KE is called stagnation enthalpy (or total enthalpy)
h0 = h + V2/2 (kJ/kg) Stagnation enthalpy Static enthalpy Kinetic energy
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Stagnation properties
• Consider a steady flow through a duct (no shaft work, heat transfer etc.).
• The steady flow energy equation for this is: h1 + V1
2/2 = h2 + V22/2
or, h01=h02
• That is in the absence of any heat and work interactions, the stagnation enthalpy remains a constant during a steady flow process.
6
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Stagnation properties
• If the fluid were brought to rest at state 2,
h1 + V12/2 = h2 =h02
• The stagnation enthalpy represents the enthalpy of a fluid when it is brought to rest adiabatically.
• During a stagnation process, the kinetic energy of a fluid is converted to enthalpy (internal energy + flow energy), which results in an increase in the fluid temperature and pressure.
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Stagnation properties
• When the fluid is approximated as an ideal gas with constant specific heats,
cpT0 = cpT +V2/2
or, T0 = T +V2/2cp
• T0 is called the stagnation temperature and represents the temperature an ideal gas attains when it is brought to rest adiabatically.
• The term V2/2cp corresponds to the temperature rise during such a process and is called the dynamic temperature.
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Stagnation properties
• The pressure a fluid attains when brought to rest isentropically is called the stagnation pressure, P0.
• For ideal gases, from isentropic relations,
)1/(1
00
)1/(
00
have, density wefor Similarly,
T
T
T
T
P
P
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Stagnation properties
s
h
Isentropic stagnation state
h
h0
Actual stagnation state
Actual state
P
P0 P0,actual
V2/2
The actual state, actual stagnation state, and isentropic stagnation state of a fluid on an h-s diagram.
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Compressor/fan performance
• Compressors are to a high degree of approximation, adiabatic.
• Compressor performance can be evaluated using the isentropic efficiency, ηc
0102
0102
ratio pressuregiven for n compressio of work Actual
ratio pressuregiven for n compressio of work Ideal
hh
hh
w
w s
c
ci
C
11
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Compressor/fan performance
T
02s
P01
P02 02
01 T01
T02s
T02
Actual and ideal compression processes
s
1: Compressor inlet
2: Compressor exit
12
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Compressor/fan performance
1
1
1
1/
1/
1/
/1
/1
0102
0102
0102
0102
0102
0102
0102
C
C
C
s
ssC
PP
TT
TT
TT
TT
hh
hh
• The isentropic efficiency is thus a function of the total pressure ratio and the total temperature ratio.
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Compressor/fan performance
• Besides isentropic efficiency, there are other efficiency definitions, stage efficiency and polytropic efficiency that are used in assessing the performance of multistage compressors.
• Stage efficiency will be discussed in detail during later lectures
• The three efficiency terms can be related to one another.
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Compressor/fan performance
• The polytropic efficiency, ηpoly, is defined as
0
0
/)1(
0
0
00
/)1(
0
0000s
/)1(
00
0
0
0
0
111
,1/for expansion binomial Using
1dT And,
constant.
gives,relation isentropic the,compressor idealan For
change pressure aldifferenti afor n compressio of work Actual
change pressure aldifferenti afor n compressio of work Ideal
P
dP
P
dP
PdP
P
dPPT
PT
dT
dT
dh
dh
dw
dw
s
sss
poly
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Compressor/fan performance
.efficiency
polytropicconstant a assuming ratio pressure with the
efficiency isentropic therelatesequation above The
1
1
1
1,
)/(/
02, and 01 statesbetween gIntegratin
1
equation, above theRewriting
/
/1
/
/
1 Therefore,
)/()1(
/1/1
)/()1(
01020102
0
0
0
0
00
00
00
00
0
0
0
0
0
0
poly
poly
C
C
C
CC
poly
sspoly
s
or
PPTT
P
dP
γ
γ
T
dT
TdT
PdP
γ
γ
TdT
TdT
dT
dT
P
dP
γ
γ
T
dT
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Turbine performance
• The flow in a turbine is also assumed to be adiabatic, though in actual engines there could be turbine blade cooling.
• Isentropic efficiency of the turbine is defined in a manner similar to that of the compressor.
/)1(
0201
0201
1
1
ratio pressuregiven for expansion of work Ideal
ratio pressuregiven for expansion of work Actual
t
t
sts
t
t
hh
hh
w
w
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Turbine performance
s
T
01
P02
P01
02 02s
T02 T02s
T01
Actual and ideal turbine processes
1: Turbine inlet
2: Turbine exit
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Turbine performance
• The polytropic efficiency, ηpoly, is defined as
00
00
00
00
0
0
0
0
0
0
/)1(
00
0
0
0
0
//)1(
/
/
/
1
Therefore, constant.
gives,relation isentropic the turbine,idealan For
change pressure aldifferenti afor work turbineIdeal
change pressure aldifferenti afor work turbineActual
PdP
TdT
TdT
TdT
dT
dT
P
dP
γ
γ
T
dT
PT
dT
dT
dh
dh
dw
dw
ss
poly
s
s
sss
poly
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Turbine performance
.efficiency
polytropicconstant a assuming ratio pressure with the
efficiency isentropic therelatesequation above The
1
1
1
1,
02, and 01 statesbetween gIntegratin
/1
/1
/1
)1(/
t
t
t
t
tt
t
poly
poly
poly
or
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Lect-2
Thermodynamics of compressors
• Simplified aero-thermodynamic analysis
• Optimised cycle design to precede the detailed component design
• Prediction of work requirements
• Efficiency of the compressor
• Enables faster design modifications
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Thermodynamics of compression
(i) Adiabatic (process 1-2’) , Pvγ=c
(ii) Isothermal process (1-2’’), Pv=c
(iii) Isochoric (Process 1-2’’’), Pv =c
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Lect-2
Thermodynamics of compressors
i) Isentropic process (1-2’)
ii) Polytropic process (1-2)
iii) Isothermal process (1-2’’)
iv) Isochoric Process (1-2’’’)
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Lect-2
Thermodynamics of compressors
X1 , X2 are the losses in the rotor and the stator respectively
Compression in terms of static parameters
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Lect-2 Thermodynamics of compressors
Compression in terms of total parameters
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Basic operation of axial compressors
• Axial flow compressors usually consists of a series of stages.
• Each stage comprises of a row of rotor blades followed by a row of stator blades.
• The working fluid is initially accelerated by the rotor blades and then decelerated in the stator passages.
• In the stator, the kinetic energy transferred in the rotor is converted to static pressure.
• This process is repeated in several stages to yield the necessary overall pressure ratio.
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Thermodynamics of multi-stage compressors
• The flow at the rotor exit with high kinetic energy is still to be converted to static pressure through diffusion.
• The exit kinetic energy of a compressor is of the same order as the entry kinetic energy and the entire work input is expected to be converted to pressure.
Rotor isentropic, stator isothermal Rotor polytropic, stator isothermal
Averaged T-s characteristics