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