Ideal Analysis Aircraft Gas Turbine Engine

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Ideal Analysis Aircraft Gas Turbine Engine
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Numbering of turbine engines
0 2 3 4
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intake compressor burner
turbine afterburner (AB) nozzle (n)
(diffuser)
(e.g., turbofan)
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Thrust Equation
Take a step back
D
Apply the momentum equation to the steady flow
through c.v. (forces time rate of change of
momentum)
P0 V0 A0
P9 V9 A9
Finternal
9
0
2
by convention use gauge pressures (pressure
referenced to Po)
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Thrust Eqn.

• Subtract Drag Force acting on the external
  surface to get net thrust (T Fint D)
• The drag is obtained by integrating the pressure
  over the external surface, i.e.,

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Lets outline some NOTATIONthat is used to
characterize gas turbines
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Total Temperature and Total Pressure

• The total temperature and pressure are the values
  reached when a steadily flowing fluid is brought
  to rest (stagnated) adiabatically reversibly
  (i.e., isentropically)
• Tt total temperature T static temperature V
  flow velocity the 1st law of thermodynamics for
  perfect gas gives
• Introduce, get
• Stagnation (Total) Pressure
• From compressible flow
• (isentropic process)

from before
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Steady flow eqn (energy egn) in absence of
g-effects (No PE)
From previous lecture
Stagnation or total enthalpy ht hV2/2
1st law
For calorically perfect gas
Stagnation or total temperature Tt TV2/2cp
Divide by cp
Static Temperature
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Total/Static Temperature Ratio and Pressure Ratio
of the Freestream (Inlet)
1
2
define tl as ratio of the burner exit
enthalpy, ht,burner exit cpTt to the ambient
enthalpy hocp,oTo
3
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Ratios across component i

• Ratio of total temperatures across a component
  ti
• Ratio of total pressures across a component pi
• where i d diffuser (intake), c compressor,
  b burner, t turbine, n nozzle, f fan

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Temperature and Pressure Component Relations
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Steps to Engine Cycle Analysis

• Objective Want to know how the engine
  performance (specific thrust fuel consumption)
  varies with changes in
• flight conditions (Mach number),
• design limits (burner exit temp),
• component performance (turbine efficiency),
• design choices (compressor pressure ratio)
• Rewrite the thrust equation in terms of total
  pressure and total temperature ratios, ambient
  pressure Po temperature To speed of sound
  ao flight Mach number Mo

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Steps to Engine Cycle Analysis

• Calculate as f(M, Ts, gas properties)

freestream
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Steps to Engine Cycle Analysis

• Find Temp ratio is

from comp. flow
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Steps to Engine Cycle Analysis

• Apply 1st law of thermodynamics to the combustor
  (adiabatic, no work done)
• Evaluate the specific thrust
• Evaluate the thrust specific fuel consumption S
  for the specific thrust and fuel-to-air ratio
  (f)
• Evaluate thermal and propulsion efficiencies.

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Assumptions

• Compression and expansion cycles are reversible
  and adiabatic (isentropic) in compressor,
  turbine, inlet (diffuser), nozzle.
• Constant Pressure Combustion fuel flow rate
  small relative to air flow rate
• Air is perfect gas with constant specific heat
• Exhaust nozzle expands gas to ambient pressure
  (Pe (?P9) Po)

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Ramjet (Ideal - Simplest)
1. Intake (Diffuser) Slows air from flight speed
V0 to V2 (P2 T2 increase)
3. Gas expansion to ambient pressure Temp.
decrease to T9
2. Conversion from chemical to thermal
energy (increases T4)
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T-s diagram of ideal ramjet
T
Tt4, Tt9
heat in
expansion
Tto, Tt2
T9
compression
heat rejected
To
0
s
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Apply the steps
1
with P9Po and
2
with g9 g0 g and R9 R0R (for ideal cycle,
no
composition change)
(will need T9/To later)
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Apply the steps
3
Nozzle outlet to inlet
Total/static freestream
Combustor outlet to inlet
Diffuser outlet to inlet
thus, or
Recall,
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Apply the steps
4
thus,
recall,
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Apply the steps
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Application of first law of thermo to cv about
the burner
Combustor
2 4
heat of reaction
where cp2cp4 cp
(needed to evaluate f)
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Apply the steps
and Tto Tt2 Totr
thus
and Tt4/Tt2 tb
and use
rewrite
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Apply the steps
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Evaluate specific thrust
1
1
from steps 2,3,4
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Apply the steps
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Evaluate specific fuel consumption S
step 5
step 7
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Efficiencies (left to you)
Thermal Propulsion Overall
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Summary
INPUTS Mo, To (K), g, cp (kJ/kg.K), hPR (KJ/kg),
Tt4 (K) OUTPUTS
(N/(kg/s)), f, S ((kg/s)/N), hT, hP, hO
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Example Performance vs M

• To217K
• g1.4
• cp1.004 kJ/(kgK)
• hPR42800kJ/kg
• Tt41600-2200K

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Specific Thrust vs Mo
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Specific Fuel Consumption vs Mo
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Fuel/air ratio (f) vs Mo
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Efficiencies vs Mo