Transcript Review AE430 Aircraft Propulsion Systems

Review AE430
Aircraft Propulsion Systems
Gustaaf Jacobs
Note
 Bring Anderson
to exam for tables.
Goals
 Understand
and analyze gas turbine
engines:

Turbojet

Turbofan (turbojet + fanned propeller)!

Ramjet
Analysis
 Analysis

Energy control volume per engine component
• Pressure and temperature changes for ideal
engine
• With efficiency definitions: pressure and
temperature changes for non-ideal engine

Control Volume over complete engine:
• Momentum balance=> thrust, propulsion efficiency
• Energy balance or thermo analysis:

Brayton cycle: Thermal efficiency
Analysis
 Detailed

component analysis
Inlets
• Subsonic flow analysis in 1D

Pressure recovery estimate
• Shock analysis in 1D inlet (converging-diverging)


Estimate of losses
External deceleration principles
• 2D shock external deceleration


Oblique shock analysis
Estimate spillage and losses
Analysis

Combustor

Qualitative idea of combustion physics
• Fuel-air ratio (stoichiometric)
• Flame speed
• Flame holding


Quantitative: pressure loss with 1D channel flow
analysis + heat addition=> not treated due to time
restrictions
Compressor/Turbine


Estimate of pressure, temperature recovery with
momentum and energy balance
Velocity triangles analysis: first order estimate of
compressor aerodynamics
Control Volume Analysis:
Basic Idea
mf
T
ma
me
T   ma  me  ve  ma va   pe  pa  Ae
T  m a 1  f  v e  v a    p e  p a  A e
Engine Performance
Parameters

Propulsion efficiency, ratio thrust power to add kinetic
energy
Tva
p 

Thermal efficiency, ratio added kinetic energy to total
energy consumption
2
2
th 


ve 2
va 2
 ma  mf   ma
2
2
ve
v
 ma a
2
2
mf QR
 ma  mf 
total  th prop
Total efficiency
Thrust Specific Fuel Consumption
TSFC 
mf
T
Thermodynamic cycles




Diagram that looks at the change of state variables at
various stage of the engine
Ideal gas turbine: Brayton cycle
Isentropic compression, constant p heat addition,
constant p heat rejection
First law of thermodynamics analysis gives expression
c T  T   c T  T   p 
for ηth
Q Q
 

1
in
th
out
Qin
p
4
1
p
cp  T4  T1 
3
2
1

 
 p2 
1
Ideal Ramjet
 Analyze
each stage using thermodynamic
analysis with energy balance and
isentropic relations to find:



P, T, p0, T0
ve, T/ma
f
Ideal Ramjet
 pt,0=pt,7,
p0=p7 => M0=M7
 T7 > T0 since heat is added during
combustion, so v7>v0 => Thrust
 Fuel to air ratio, use first law:
Non-ideal ramjet

Non-isentropic compression and expansion:
losses lead to lowered total pressure and
temperature

Define total pressure ratios before and after
components to quantify the efficiency:
 rc, rn,rd
Non-Ideal turbojet

Major difference with ramjet ptotal is not constant like in ramjet but
increases and decrease in compressor and turbine.

To find these ratios work from front to back through each stage
Specific: compressor and turbine power are the same so (first law)

Definition of component efficiencies

E.g. diffuser
d 

T0,2s  Ta
T0,2  Ta
Relates actual total temperature increase to an
isentropic temperature increase
 The isentropic temperature can be related to the
total pressure using isentropic relations
 The total pressure distribution is determined
from front to back.
 Each stage has an effiiciency like this.
Turbofan
 Example
on blackboard.
Detailed analysis of components
Intakes


Convert kinetic energy to pressure
Subsonic



External acceleration or decelleration depends on intake design
and speed of aircraft
High speed: spillage. Low speed: stall.
Diffuser design: prevent stall: use computational (XFOIL, MSES)
and experimental validation to design
Supersonic intake







1D: converging-diverging nozzle
Ideal: isentropic decelleration supersonic to
throat, subsonic after throat
Not possible in practice
Shocks in nozzle
Possible design: shock close to throat and M~1
at throat
Need overspeeding to swallow shock in throat.
Kantrowitz-Donaldson: design condition is shock
swallowing condition.
Supersonic diffuser
 2-D


nozzle
Use multiple oblique shocks to slow flow
down with small losses in total pressure
Use oblique shock analysis
Combustor + Compressor
 Discussed
in last classes