Exhaust properties estimation of the JJ-1400 Turbojet
Given From Jet-Joe:
RPMidle 42000 rpmrpmrpmrpm EGTnominal 680 CCCC =T9 680 CCCC 953.15 KKKK
RPMmax 160000 rpmrpmrpmrpm Lubricant Turbine oil: 3%-5%
Fuel: Jet-A Kerosene Fmax 14 lbflbflbflbf (max thrust) 1.4
=Qf 200 mLmLmLmL
min 3.333 106
mmmm3
ssssfuel consuption
Measured Geometry:
D9 45.4 mmmmmmmm D5 59.5 mmmmmmmm =Do +89.9 49.1
2mm 69.5 mmmmmmmm
hPR_f 43.1 106 JJJJ
kgkgkgkglow heating value =f 0.81
gmgmgmgm
cmcmcmcm3
810 kgkgkgkg
mmmm3
=m'f Qf f 0.0027 kgkgkgkg
ssssRair 287
JJJJ
kgkgkgkg KKKK
Cycle Analysis:
Knowing thrust and assuming as a first approximation using momemtum equation that inlet velocity is zero, we get:
F m'9 V9 m'o Vo
9 0.365 kgkgkgkg
mmmm3
assuming atm pressure
9 1.34 cp_9 1130 JJJJ
kgkgkgkg KKKK
=A9
4D9
2 0.00162 mmmm2 =a9 9 Rair T9 605.444
mmmm
ssss
=V9
Fmax
9 A9324.646
mmmm
ssss=M9
V9
a90.536 =Tt9 +T9
V92
2 cp_9999.785 KKKK
n Tt9
Tt51 Tt5 Tt9 assuming adiabatic flow through nozzle
=A5
4D5
2 0.00278 mmmm2
from continuity assuming same density : =V5
V9 A9
A5189.011
mmmm
ssss
=T5 Tt5 V5
2
2 cp_9983.977 KKKK
2nd Iteration
=m'9 A9 9 V9 0.192 kgkgkgkg
ssss=m'o m'9 m'f 0.189
kgkgkgkg
ssss
F m'9 V9 m'o Vo Ao
4Do
2
=o 1.181 kg
m31.181
kgkgkgkg
mmmm3
=Vo m'o
o Ao42.212
mmmm
ssss
=V9
+Fmax m'o Vo
9 A9344.828
mmmm
ssss
3rd Iteration
=m'9 A9 9 V9 0.204 kgkgkgkg
ssss=m'o m'9 m'f 0.201
kgkgkgkg
ssss
F m'9 V9 m'o Vo Ao
4Do
2
=o 1.181 kg
m31.181
kgkgkgkg
mmmm3
=Vo m'o
o Ao44.874
mmmm
ssss
=V9
+Fmax m'o Vo
9 A9347.367
mmmm
ssss
4th Iteration
=m'9 A9 9 V9 0.205 kgkgkgkg
ssss=m'o m'9 m'f 0.203
kgkgkgkg
ssss
F m'9 V9 m'o Vo Ao
4Do
2
=o 1.181 kg
m31.181
kgkgkgkg
mmmm3
=Vo m'o
o Ao45.209
mmmm
ssss
=V9
+Fmax m'o Vo
9 A9347.696
mmmm
ssss
5th Iteration
=m'9 A9 9 V9 0.205 kgkgkgkg
ssss=m'o m'9 m'f 0.203
kgkgkgkg
ssss
F m'9 V9 m'o Vo =Ao
4Do
2 0.00379 mmmm2
=o 1.181 kg
m31.181
kgkgkgkg
mmmm3
=Vo m'o
o Ao45.252
mmmm
ssss
=V9
+Fmax m'o Vo
9 A9347.739
mmmm
ssss
6th Iteration
=m'9 A9 9 V9 0.205 kgkgkgkg
ssss=m'o m'9 m'f 0.203
kgkgkgkg
ssss
F m'9 V9 m'o Vo Ao
4Do
2
=o 1.181 kg
m31.181
kgkgkgkg
mmmm3
=Vo m'o
o Ao45.258
mmmm
ssss
=V9
+Fmax m'o Vo
9 A9347.744
mmmm
ssss
Now we calculate the final total properties:
=Tt9 +T9 V9
2
2 cp_9
1.007 103 KKKK =M9 V9
a90.574
Tt5 Tt9 from continuity assuming same density we have following estimation :
=V5 V9 A9
A5202.459
mmmm
ssss
=T5 Tt5 V5
2
2 cp_9988.52 KKKK
Now the calculations to estimate the real static temperature, pressure, density and velocity @5:
Assuming c Pt3
Pt22.8 c 2.8 cp 1004
JJJJ
kgkgkgkg KKKK
c Tt3
Tt2=c c
1
1.342
Temperatures
=T0 25 CCCC 298.15 KKKK =Tt2 +T0 Vo
2
2 cp299.17 KKKK rblade.mean 10 mmmmmmmm
=Tt3 c Tt2 401.493 KKKK =Vblade.mean RPMmax rblade.mean 167.552 mmmm
ssss
=V3+Vblade.mean
2 Vo2 173.556
mmmm
ssss
=T3 Tt3 V3
2
2 cp386.492 KKKK
Pressures
P0 101 kPakPakPakPa
=Pt2 +P0 o Vo
2
2102.21 kPakPakPakPa
=Pt3 Pt2 c 286.187 kPakPakPakPa 3 2.27 kgkgkgkg
mmmm3
=P3 Pt3 3 V3
2
2251.998 kPakPakPakPa
=qin hPR_f m'f 116.37 kWkWkWkW
=P4 P3 251.998 kPakPakPakPa
qin hPR m'f +m'o m'f cp T4 T3
=T4 +T3 qin
+m'o m'f cp950.597 KKKK =T4 677.447 CCCC =T5 988.52 KKKK
b Tt4
Tt3T9
T0=b
T9
T03.197 =Tt4 Tt3 b
1.284 103 KKKK
=M4
Tt4
T412
11.323
=Tt5 1.007 103 KKKK =Pt4 P4
+1
1
2M4
2
1
720.817 kPakPakPakPa
=Pt5 Tt5
Tt4
1
Pt4 307.961 kPakPakPakPa
=Pt5
Pt40.427 =
Pt4
Pt52.341
Iterative calculations to get t5, p5 and V5:
1st
5 0.58136 kgkgkgkg
mmmm3
=P5 Pt5 5 V5
2
2296.047 kPakPakPakPa
=V5 V9 A9 o
A5 5411.285
mmmm
ssss=o 1.181
kgkgkgkg
mmmm3
=T5 Tt5 V5
2
2 cp_9931.81 KKKK =Tt5 1006.6571 KKKK
2nd
5 1.11 kgkgkgkg
mmmm3
=P5 Pt5 5 V5
2
2214.08 kPakPakPakPa
=V5 V9 A9 o
A5 5215.409
mmmm
ssss=T5 Tt5
V52
2 cp_9986.126 KKKK
3rd
5 0.87 kgkgkgkg
mmmm3
=P5 Pt5 5 V5
2
2287.777 kPakPakPakPa
=V5 V9 A9 o
A5 5274.833
mmmm
ssss=T5 Tt5
V52
2 cp_9973.235 KKKK
4th
5 1.03 kgkgkgkg
mmmm3
=P5 Pt5 5 V5
2
2 2.691 105 PaPaPaPa
=V5 V9 A9 o
A5 5232.14
mmmm
ssss=T5 Tt5
V52
2 cp_9982.812 KKKK
5th
5 0.9922 kgkgkgkg
mmmm3
=P5 Pt5 5 V5
2
2 2.812 105 PaPaPaPa
=V5 V9 A9 o
A5 5240.984
mmmm
ssss=T5 Tt5
V52
2 cp_9980.961 KKKK
6th
5 0.9896 kgkgkgkg
mmmm3
=P5 Pt5 5 V5
2
2279.227 kPakPakPakPa
=V5 V9 A9 o
A5 5241.617
mmmm
ssss=T5 Tt5
V52
2 cp_9980.826 KKKK
Kinetic Power Available from the fluid
=Ke 1
2m'9 V9
2 12.423 kWkWkWkW