• Recap: Lecture 27, 15th October 2024, 1135-1225
hrs.
– Brayton cycle for jet propulsion systems
– Actual/real Brayton cycle
• Component performances: compressor and turbine efficiencies
– Ideal Brayton cycle for jet engine without and with reheat
– Jet engine performance parameters
• Thrust
• Efficiency: propulsion, thermal and overall
• SFC: TSFC, BSFC
• Extra-lecture: Saturday, 19-October-2024, 0930-1100 hrs,
Aero Annex Seminar Hall
Lect-7
Ideal cycle for jet engines
Combustion chamber/burner
Diffuser Compressor Turbine Nozzle
a 1 2 3 4 5 6 7
Afterburner
Schematic of a turbojet engine and
station numbering scheme 2
Ideal cycle for jet engines
4
T
3
7
2
a
Ideal turbojet cycle (without afterburning)
on a T-s diagram
3
Ideal cycle for jet engines
• For cycle analysis we shall take up each component and
determine the exit conditions based on known inlet parameters.
• Intake: Ambient pressure, temperature and Mach number are
known, Pa, Ta and M
• Intake exit stagnation temperature and pressure are
determined from the isentropic relations:
æ g -1 2 ö
T02 = Ta ç1 + M ÷
è 2 ø
g /(g -1)
æ T02 ö
P02 = Pa çç ÷÷
è Ta ø 4
Ideal cycle for jet engines
• Compressor: Let the known compressor pressure ratio be
denoted as
P03 = p c P02
T03 = T02 (p c )
(g -1) / g
• Combustion chamber: From energy balance,
(1+ f )h04 = h03 + fQR
T04 / T03 −1
or, f =
QR / c pT03 − T04 / T03
• Hence, we can determine the fuel-air ratio.
5
Ideal cycle for jet engines
• Turbine: Since the turbine produces work to drive
the compressor, Wturbine = Wcompressor
(m! a + m! f )c p (T04 − T05 ) = m! a c p (T03 − T02 )
or, (1+ f )(T04 − T05 ) = (T03 − T02 )
T05 = T04 − (T03 − T02 ) / (1+ f )
γ /(γ −1)
⎛T ⎞
Hence, P05 = P04 ⎜⎜ 05 ⎟⎟
⎝ T04 ⎠
For an ideal combustion chamber, P04 = P03 6
Ideal cycle for jet engines
• Nozzle: With no afterburner, T06=T05, P06=P05
Therefore, the nozzle exit kinetic energy,
ue2
= h07 - h7
2
Since, h07 = h06
ue = 2c pT06 [1 - (P / P
a 06 )( g -1) / g
]
• Thrust, TSFC and efficiencies can now be determined
using the formulae derived earlier.
7
Ideal cycle for jet engines
• Thrust, Á = m
a [(1 + f )ue - u ] + ( Pe - Pa ) Ae
If ( Pe - Pa ) Ae is negligible,
Á = m a [(1 + f )ue - u ]
m f m f
• TSFC = »
Á m a [(1 + f )ue - u ]
Áu
• Propulsion efficiency, h P =
[
m a (1 + f )(ue2 / 2) - u 2 / 2 ]
• Thermal efficiency, hth =
[(1 + f )(u 2
e/ 2) - u 2 / 2 ]
fQR
8
Lect-7
Turbofan engine
• Propulsion efficiency is a function of the exhaust velocity to
flight speed ratio.
• This can be increased by reducing the effective exhaust
velocity.
• In a turbofan engine, a fan of a larger diameter than the
compressor is used to generate a mass flow higher than
the core mass flow.
• This ratio (m
cold / m hot ) is called the bypass ratio.
• Turbofan engines have a higher propulsion efficiency as
compared with turbojet engines operating in the same
speed range.
9
Lect-7
Ideal turbofan engine
2’ 3’ Secondary 7’
Diffuser nozzle
Fan m! C Combustion chamber/burner
Compressor Turbine
m! a m! f Primary nozzle
= m! C + m! H
m! H
a 1 2 3 4 5 6 7
Schematic of an unmixed turbofan
engine and station numbering scheme 10
Lect-7
Ideal turbofan engine
Diffuser
2’ 3’ 7’ Nozzle
Fan m! C Combustion chamber/burner
Compressor Turbine
m! a m! f
= m! C + m! H
m! H
a 1 2 3 4 5 6 7
Schematic of a mixed turbofan engine
and station numbering scheme 11
Un-mixed turbofans (high bypass civil engine)
Mixed turbofans (low bypass military engine)
Lect-8
Typical component efficiencies
Component Figure of Type Value
merit
Diffuser πd Subsonic 0.95-0.98
Supersonic 0.85-0.95
Compressor ηC - 0.87-0.93
Burner ηb - 0.96-0.99
πb 0.90-0.95
Turbine ηt Uncooled 0.88-0.94
Cooled 0.87-0.93
Afterburner ηab - 0.96-0.99
πab 0.90-0.95
Nozzle ηn - 0.95-0.98
Mechanical ηm - 0.96-0.99
13
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
