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MAE 4261: AIR-BREATHING ENGINES
Thermodynamics Review and Cycle Analysis Overview
September 1, 2009
Mechanical and Aerospace Engineering DepartmentFlorida Institute of Technology
D. R. Kirk
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HEAT ENGINE: PROPULSION CHAIN
ChemicalEnergy
Heat
(ThermalEnergy)
MechanicalPower
Mech.
Power toGasFlow
ThrustPower
The overall efficiency for the propulsion chain is given by:
Combustion Thermal Propulsive
Thrust=F
speedFlighto
u
fueljetforJ/kg710x4.3=reaction)of(heatcombustionofHeatcomb
h
rateflowFuelf
m
comb
0=overall
hf
m
FU
usageenergychemicalofRate
powerThrust
forpayWhat we
getWhat we
propulsivemechthermalcombustionoverall
Mechanical
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CONCEPTS / TOOLS FOR ENGINE IDEAL CYCLE ANALYSIS
Ideal gas equation of state, p = rRT
One-dimensional gas dynamics
Concepts of stagnation and static quantities (temperature, pressure, etc.)
Relations between Mach number and thermodynamic properties
Thermodynamics of propulsion cycle
Make use of 1st and 2nd Laws of Thermodynamics
Behavior of useful quantities: energy, entropy, enthalpy
Relations between thermodynamic properties in a reversible (lossless) process
Isentropic = reversible + adiabatic
Properties of cycles (it is cyclic)
Air starts at atmospheric pressure and temperature and ends up at atmospheric pressureand temperature
Definition of Open vs. Closed Cycles
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STAGNATION QUANTITIES DEFINED
Quantities used in describing engine performance are the stagnation pressure,
enthalpy and temperature
Stagnation enthalpy, ht , enthalpy state if stream is decelerated adiabatically to zerovelocity
2
2
11or
2
2
2
11
2
1
)2(
21
2
2
2
2
MT
tT
a
u
T
tT
RTa
R
pc
Tpc
u
T
tT
pc
uT
tT
Tpch
uh
th
Ideal gas
Stagnation temperature
Speed of sound
Total to static temperature ratio
in terms of Mach number
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FOR REVERSIBLE + ADIABATIC = ISENTROPIC PROCESS
flowspeedlowforEquation"Bernouli"
2
2
1
gettotheorembinomialtheusingexpand,12For
1
2
2
11
velocity)zeroally toisentropicddecelerateisstreamifpressureis(
pressurestagnationthedefines1
constant)1/(
findweusing
constant
upt
p
M
Mp
tp
tp
T
T
p
tp
T
pRTp
P
t
r
r
r
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RECAP ON THERMODYNAMICS: 1st LAW
First law (conservation of energy) for a system: chunk of matter
of fixed identity
E0 = Q - W
Change in overall energy (E0 ) = Heat in - Work done
E0 = Thermal energy + kinetic energy ...
Neglecting changes in kinetic and potential energy
E = Q - W ; (Change in thermal energy)
On a per unit mass basis, the statement of the first law is thus:
e = q - w
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RECAP ON THERMODYNAMICS: 2nd LAW
The second law defines entropy,s,by:
ds dqreversible
T
Where dqreversible is the increment of heat received in a reversible
process between two states
The second law also says that for any process the sum of the
entropy changes for the system plus the surroundings is equal
to, or greater than, zero
ssystem ssurroundings 0Equality only exists in a reversible (ideal) process
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REPRESENTING ENGINE PROCESS
IN THERMODYNAMIC COORDINATES
First Law:E = Q - W, where E is the total energy of the parcel of air.
For a cyclic process Eis zero (comes back to the same state)
Therefore: Q (Net heat in) = W(Net work done)
Want a diagram which represents the heat input or output.
A way to do this is provided by the Second Law
Tdsreversible
dq
where ds is the change in entropy of a unit mass of the parcel and
dq is the heat input per unit mass
Thus, one variable should be the entropy ,s
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STEADY FLOW ENERGY EQUATION (I)
Shaft work
Heat input
Mass flow
Device
1 2
ht 2- ht 1= q - w shaft
qis heat input/unit mass
wshaft is the shaft work / unit mass
For any device in steady flow
previouslydefinedenthalpystagnationtheis2/quantityThe
doneshaft workofRate-inheatofRate=
2
shaft12
uhh
WQhhm
t
tt
Per unit mass flow rate:
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STEADY FLOW ENERGY EQUATION (II)
The form of the steady flow energy equation shows that enthalpy, h:
h = e + pv = e + p/r
Natural variable to use in fluid flow-energy transfer processes.
For an ideal gas with constant specific heat, dh = cpdT.
Changes in enthalpy are equivalent to changes in temperature.
To summarize, the useful natural variables in representing gas turbine engine
processes are h,s (or T, s).
Represent thermodynamic cycle (Brayton) for gas turbine engine on a T,s diagram
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THERMODYANMICS: BRAYTON CYCLE MODEL
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GAS TURBINE ENGINE COMPONENTS
Inlet: Slows, or diffuses, the flow to the compressor
Fan/Compressor: (generally two, or three, compressors in series) does work onthe air and raises its stagnation pressure and temperature
Combustor: Heat is added to the air at roughly constant pressure
Turbine: (generally two or three turbines in series) extracts work from the air to
drive the compressor or for power (turboshaft and industrial gas turbines)
Afterburner: (on military engines) adds heat at constant pressure
Nozzle: Raises the velocity of the exiting mass flow
Exhaust gases reject heat to the atmosphere at constant pressure
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THERMODYNAMIC CHARACTERISTICS
OF COMPONENTS (IDEAL COMPONENTS)
0=sexchange,heatno,shaft workNo:nozzleExhaust
losslessadiabatic,0s
,turbinefromoutputwork0,>shaft
wwh:Turbine
input)(heatqh:rafterburneandCombustor
losslessadiabatic,0s
,compressorinput towork0,wwh:Compressor
0h:Inlet
shaftt
int
shaftshaftt
t
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THERMODYNAMIC MODEL OF GAS TURBINE ENGINE CYCLE
[Cravalho and Smith]
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SCHEMATIC OF CONDITIONS THROUGH A GAS TURBINE
[Rolls-Royce]
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NOMINAL PRESSURES AND TEMPERATURES FOR A
PW4000 TURBOFAN [Pratt&Whitney]
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REVIEW OF STATION LOCATIONS