3. Goals
Understand and analyze gas turbine
engines:
Turbojet
Turbofan (turbojet + fanned propeller)!
Ramjet
4. 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
6. 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
7. Control Volume Analysis:
Basic Idea
T
a
m e
m
f
m
a e e a a e a e
T m m v m v p p A
a e a e a e
T m 1 f v v p p A
8. Engine Performance
Parameters
Propulsion efficiency, ratio thrust power to add kinetic
energy
Thermal efficiency, ratio added kinetic energy to total
energy consumption
Total efficiency
Thrust Specific Fuel Consumption
a
p 2 2
e a
a f a
Tv
v v
m m m
2 2
2 2
e a
a f a
th
f R
v v
m m m
2 2
m Q
total th prop
f
m
TSFC
T
9. 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
for ηth
1
p 4 1 p 3 2in out 1
th
in p 4 1 2
c T T c T TQ Q p
1
Q c T T p
10. Ideal Ramjet
Analyze each stage using thermodynamic
analysis with energy balance and
isentropic relations to find:
P, T, p0, T0
ve, T/ma
f
11. 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:
12. 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 ramjet
13. 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)
Non-Ideal turbojet
14. Definition of component efficiencies
E.g. diffuser
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.
0 ,2 s a
d
0 ,2 a
T T
T T
17. 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
18. 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.
19. Supersonic diffuser
2-D nozzle
Use multiple oblique shocks to slow flow
down with small losses in total pressure
Use oblique shock analysis
