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Parametric Study of Turbofan Engine Performance
P M V Subbarao
Professor
Mechanical Engineering Department
Its Time to think about fuel Economy……
Thrust Specific Fuel Consumption TSFC
totalT
fuel
F
mTSFC
,
accoldjetachotjet
jetcoldcoreachotjetcore
fuel
VVVVf
f
VVmVVfm
mTSFC
1
1
Effect of Fan Bypass Ratio
r0,p,fan=2.5 r0,p,comp=15 T0max=1200K Mac =0.75
TSF
CCombined Effect of Fan & Compressor Pressure Ratios
T0max=1200K Mac =0.75
ac
total
V
S
Combined Effect of Fan & Compressor Pressure Ratios
T0max=1200K Mac =0.75
Combined Effect of Fan & Compressor Pressure Ratios
TS
FC
Compressor Pressure Ratio
Fan Pressure Ratio
Combined Effect of Fan & Compressor Pressure Ratios
Spe
cifi
c T
hrus
t kN
.s/k
g
Compressor Pressure Ratio
Fan Pressure Ratio
r0p,fan=1.5
r0p,fan=2.0
r0p,fan=4.0
r0p,fan=3.5 r0p,fan=4.5r0p,fan=3.0
Optimum Fan Pressure Ratio for Fuel Economy
Fan Pressure Ratio
TSF
C
r0,p,comp=24 T0max=1800K Mac =0.9
Optimum Fan Pressure Ratio for CompactnessS
peci
fic
Thr
ust k
N.s
/kg
Fan Pressure Ratio
r0,p,comp=24 T0max=1800K Mac =0.9
Optimum Fan Pressure Ratio for Propulsion Efficiency
Fan Pressure Ratio
r0,p,comp=24 T0max=1800K Mac =0.9
Fan Effects on Thrust Ratio
Fan Pressure Ratio
r0,p,comp=24 T0max=1800K Mac =0.9
Thrust Ratio : r0,p,fan=2.5 & Mac=0.75
Compressor Pressure Ratio
Turbofan with After Burner
Effect of After Burner : Compactness
ac
total
V
S
Turbojet w AB
Turbojet w/o AB
Turbofan w AB
Turbojfan w/o AB
For same level of life & Energy
Effect of After Burner : Fuel EconomyT
SFC
Turbofan w/o AB
Turbojet w/o AB
Turbojet w AB
Turbofan w AB
Optimization Analysis of Turbofan
• Operational Parameters : Flight Mach number & Ambient conditions.
• Design Variables : Fan Pressure Ratio, Bypass Ratio, Compressor Pressure Ratio, Combustion Chamber Temperature Ratio.
• Maximization of specific thrust is not an important issue.
• Fuel economy is the main focus for optimization.
Thrust Specific Fuel Consumption TSFC
totalT
fuel
F
mTSFC
,
accoldjetcoreachotjetcore
fuel
VVmVVfm
mTSFC
1
accoldjetachotjet VVVVf
fTSFC
1
For small fuel/air ratios:
Assume that the value of f is constant:
11ac
coldjet
ac
hotjetac
V
V
V
Vf
VTSFC
accoldjetachotjet VVVV
fTSFC
For maximum fuel economy, maximize the denominator.
Defined D as
11:ac
coldjet
ac
hotjet
V
V
V
VDMaximize
Fan Effects : Fan Pressure Ratio & Bypass Ratio.
Core Effects : Bypass Ratio, Compressor Pressure Ratio & Combustion Chamber Temperature Ratio.
Optimal Selection of Bypass Ratio
0
11
ac
coldjet
ac
hotjet
V
V
V
V
D
As fan handles the entire air intake, Vcoldjet is independent of bypass ratio
01
ac
coldjetac
hotjet
V
VV
V
Rewrite as:
01
2
1
2
ac
coldjetac
hotjet
ac
hotjet V
VV
V
V
V
12
11
1
2 2,0,0,0
,0,0
,0acturbpcomppfanp
comppfanp
cchotjet McV
1
2
11
1
2 2,0,0,0
,0,0
,0
22
acturbpcomppfanpcomppfanp
cc
acac
hotjet MV
c
V
V
1
2
11
1
2 2,0,0,0
,0,0
,0
22
acturbpcomppfanpcomppfanp
cc
acac
hotjet MV
c
V
V
cc
fanpcomppfanpturbp
f ,0
,0,0,0,0
1
1111
turbp
accomppfanpcomppfanp
cc
acac
hotjet MV
c
V
V ,02,0,0
,0,0
,0
22
2
11
1
2
cc
fanpturbp
f ,0
,0,0
1
1
cc
fanpaccomppfanp
comppfanp
cc
acac
hotjet
fM
V
c
V
V
,0
,02,0,0
,0,0
,0
22
1
1
2
11
1
2
01
2
1
2
ac
coldjetac
hotjet
ac
hotjet V
VV
V
V
V
cc
fanpaccomppfanp
comppfanp
cc
acac
hotjet
fM
V
c
V
V
,0
,02,0,0
,0,0
,0
22
1
1
2
11
1
2
1
2
11
1
2 2,077 acfanpcccoldjet McRTMV
12
11
1
2 2,0,0,0
,0,0
,0acturbpcomppfanp
comppfanp
cchotjet McV
011
1
2
11
1
2
2
1
,0
,02,0,0
,0,0
,0
2
ac
coldjet
cc
fanpaccomppfanp
comppfanp
cc
ac
ac
hotjet V
V
fM
V
c
V
V
01
1
2
11
1 ,0
,02,02
accoldjethotjetcc
fanpac
cc VVVf
Mc
cc
fanpac
ccaccoldjethotjet f
Mc
VVV,0
,02,02
1
1
2
11
1
Condition for optimum bypass ratio at minimum TSFC.
Solve above equation for optimum bypass ratio to give minimum specific fuel consumption.Further use of opt to calculate velocities of cold and hot jets will gives ? ????
Maximum Fuel Economy : Effect of Compressor Pressure Ratio
opt
r0,p,comp
T04=1700Kr0,p,fan=2.0Mac=0.9
Maximum Fuel Economy : Effect of Fan Pressure Ratio
opt
r0,p,fan
T04=1700Kr0,p,comp=24.0Mac=0.9
Maximum Fuel Economy : Effect of Flight Mach Number
opt
ac
T04=1700Kr0,p,comp=24.0
r0,p,fan=3.0
r0,p,fan=2.0
Optimal Selection of Fan Pressure Ratio
0
11
,0,0
fanp
ac
coldjet
ac
hotjet
fanp
V
V
V
V
D
0
11
,0,0
fanp
ac
coldjet
fanp
ac
hotjet
V
V
V
V
ch VV 77
Maximum Fuel Economy : Effect of Bypass Ratio
rfan,opt
r0,p,comp=24.0Mac=0.9
Maximum Fuel Economy : Effect of Compressor Pressure Ratio
rfan,opt
rcomp
T04=1700K=4.0Mac=0.9
rfan,opt
TSFC
8
7
6
5
4
3
21 2 3 4 5 6 7 8 9
16.5
16
15.5
15
14.5
14
13.513
17
Contours of Constant TSFC
Contours of Constant Specific Thrust
rfan,opt
8
7
6
5
4
3
21 2 3 4 5 6 7 8 9
500
450
400
350300
280260
240220
200
Mixed Flow Turbofan Engine
1 2 3 4 56h
76c
8
0306c pp
