homework 6 - utah state university
TRANSCRIPT
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MAE 6530 - Propulsion Systems II
Homework 6.2
29
Consider the TurboFan Engine whose Block Diagram is Shown Below
Diffuser Compressorcore3
fan3
Bypass
TurbineCombustorCore Exhaust
Fan
Bypass Exhaust
fan3
Fan
Bypass ExhaustBypass
core4
core5
coreexit
fanexit
fanexit
∞
1
2
With Following Conditions Aircraft Mach Number: 0.70Aircraft Altitude: 6 kmBypass Ratio: 2Fan Pressure Ratio: 2Compressor Ratio: 6Burner Outlet Temperature: 1700 K Fuel: JP4 à hf = 42.68 MJ/kg
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MAE 6530 - Propulsion Systems II
Homework 6.2 (2)
30
Assume the Following Component Propertiesi) Diffuser, Compressor, Fan, Turbine, Nozzle ~ Isentropicii) Nozzle exit flow is NOT mixediii) Combustor is 35% efficient àiv) Fuel massflow is NOT negligiblev) Mean specific heats, gamma are constant across engine constant àvi) Fan, Core Nozzle Exits Optimized for Altitude
Diffuser Compressorcore3
fan3
Bypass
TurbineCombustorCore Exhaust
Fan
Bypass Exhaust
fan3
Fan
Bypass ExhaustBypass
core4
core5
coreexit
fanexit
fanexit
∞
1
2
ηb =!Q3−4!mfuel ⋅hf
= τ f ⋅Cp ⋅T∞hf γ≈1.4
Cp ≈1004.96J /kg−K
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MAE 6530 - Propulsion Systems II
Homework 6.2 (3)
31
Calculatei) Normalized Thrustii) % of Thrust delivered by Core Flowiii) % of Thrust delivered by Bypass Flowii) Ratio of Bypass Thrust to Core Thrustiii) Normalized Specific Impulseiv) TSFC lbm/lbf-hrv) Bypass Ratio for Optimal Ispvi) Optimal TSFC
Diffuser Compressorcore3
fan3
Bypass
TurbineCombustorCore Exhaust
Fan
Bypass Exhaust
fan3
Fan
Bypass ExhaustBypass
core4
core5
coreexit
fanexit
fanexit
∞
1
2
T= Fthrustp∞ ⋅ A∞
I=Isp ⋅g0c∞
TSFC= 1g0 ⋅ Isp
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turbofan_cycle_..0_solution.vi/Users/stephenwhitmore/Desktop/MAE .@AB/MAE_.@AB_Web/New_Course/Section./turbofan_cycle_..0_solution.vi
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Page I
B.J
Mach Number
.
Altitude, km
N.0.LE+J
Fuel Enthalpy, Kj/kg
IBBN.Q.
Cp, J/kg-K
I.N
Gamma
IJBB
Max Burner Temperature, K
.
Core Compressure Pressure Ratio
0
Fan Pressure Ratio
0
Bypass ratio
B.A@
Ccombustion Efficiency
Freestream Conditions
ALI.N@
Qc, psf
Pinf, psfNNL.NJ
Tinf, RJ0..JB
Vtrue, ft/secAAJ.QQ
Qbar, psf
IQ.LN.QLBB
Altitude, ft
IA...L@
P0_inf, psf
NQ0.N0
T0_inf, R
Flight Parameters Engl
IL.0.
Qc, kPa
NJ.IL
Pinf, kPa
00I.@B
Vtrue, m/secI..IL
Qbar, kPa
0NQ.I@
Tinf, KI.I0L.
CpMax
P0_inf, kPa
0JA.@J
T0_inf, K
Flight Parameters Metric
..L0A0
Tau Lambda
I.BQL
Tau r
I...L@I
Tau Ccore
I.0IQBIAJ
Tau C fan
B......J
Bypass Fraction
@Q..@QQ
Tau f
AI.J@LI
Air/fuel ratio, f
B.LAJABA
Tau turb
B.BAINLL
Fuel/Air ratio, f 2
NonDimensional Parameters 2
N.@BNJN
Core Ve/Vinf
I.L@LN@
Fan Ve/Vinf
B.LJJI00
Core Momentum Thrust
B.AQ0@QQ
Fan Momentum Thrust
I.0.QJ0
Total Normalized Thrust
NI.IN.Q
Normalized Specific Impulse
IAB0I.L
Specific Thrust, N-s/kg
0.JIII@
TSFC, lbm/(lbf-hr)
B.NNJ@QQ
Ratio Bypass to Core Thrust B..QBJQQ
% Core Thrust
B.ABQ0BI
% Bypass Thrust
B.0NNQNI
(Vfan-Vinf)/(Vcore-Vinf)
IA0J.L@
ISP, SEC
AI..NJ0
cinf, m/sec
J..JQN0E-@
TSFC, kg/N-sec
Normalized Thrust, Isp
Yes
A0..JJ
Value
Ignore A/F ratio in Turbine Calculation
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turbofan_cycle_HW0.2_opt.vi/Users/stephenwhitmore/Desktop/MAE 0BCD/MAE_0BCD_Web/New_Course/Section0/turbofan_cycle_HW0.2_opt.vi
Last modified on J2/K/2D at JDLMJ AMPrinted on J2/K/2D at JDLM0 AM
Page J
D.K
Mach Number
0
Altitude, km
M.20PE+K
Fuel Enthalpy, Kj/kg
JDDM.R0
Cp, J/kg-K
J.M
Gamma
JKDD
Max Burner Temperature, K
0
Core Compressure Pressure Ratio
2
Fan Pressure Ratio
JD.J0
Bypass ratio
D.CB
Ccombustion Efficiency
Freestream Conditions
CPJ.MB
Qc, psf
RPB.MD
Pinf, psfMMP.MK
Tinf, RK20.KD
Vtrue, ft/secCCK.RR
Qbar, psf
JR0PM.RPDD
Altitude, ft
JC00.PB
P0_inf, psf
MR2.M2
T0_inf, R
Flight Parameters Engl
JP.20
Qc, kPa
MK.JP
Pinf, kPa
22J.BD
Vtrue, m/secJ0.JP
Qbar, kPa
2MR.JB
Tinf, KJ.J2P0
CpMax
0B.MB
P0_inf, kPa
2KC.BK
T0_inf, K
Flight Parameters Metric
0.P2C2
Tau Lambda
J.DRP
Tau r
J.00PBJ
Tau Ccore
J.2JRDJCK
Tau C fan
D.RJDCRM
Bypass Fraction
BR.0BRR
Tau f
JJP.JM
Air/fuel ratio, f
D.BKMBCM
Tau turb
D.DDPM0MB2
Fuel/Air ratio, f 2
NonDimensional Parameters 2
J.MJCCM
Core Ve/Vinf
J.PBPMB
Fan Ve/Vinf
D.D2KPDKP
Core Momentum Thrust
D.BC0JC
Fan Momentum Thrust
D.B0CRCP
Total Normalized Thrust
0K.RPCC
Normalized Specific Impulse
2JBJM.P
Specific Thrust, N-s/kg
J.0MDR2
TSFC, lbm/(lbf-hr)
JR.2KRR
Ratio Bypass to Core Thrust D.DMRCJ
% Core Thrust
D.RBD0R
% Bypass Thrust
2.DK0PP
(Vfan-Vinf)/(Vcore-Vinf)
2JRC.PR
ISP, SEC
CJ0.MK2
cinf, m/sec
M.0MKR0E-B
TSFC, kg/N-sec
Normalized Thrust, Isp
Yes
C2.0KK
Value
Ignore A/F ratio in Turbine Calculation
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bypass_ratio_turbo_plot_HW/.1.vi/Users/stephenwhitmore/Desktop/MAE /@AB/MAE_/@AB_Web/New_Course/Section//bypass_ratio_turbo_plot_HW/.1.vi
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Page J
B.N
Mach Number
/
Altitude, km
O.1/KE+N
Fuel Enthalpy, Kj/kg
JBBO.R/
Cp, J/kg-K
J.O
Gamma
JNBB
Max Burner Temperature, K
/
Core Compressure Pressure Ratio
1
Fan Pressure Ratio
B.A@
Ccombustion Efficiency
Freestream Conditions
B.J
Minimum Bypass Ratio
1@
Maximum Bypass Ratio
JBBB
# of Points
Bypass Ratio
Non
dim
ensi
onal
Isp
NB
AB
A@
OB
O@
@B
@@
/B
/@
Bypass ratioJ1B 1 O / K JB
Normalized Specific Impulse
/.K1A1
Tau Lambda
J.BRK
Tau r
J.//K@J
Tau Ccore
J.1JRBJAN
Tau C fan
B.RJ1N1K
Bypass Fraction
@R./@RR
Tau f
J1J.1RR
Air/fuel ratio, f
B.@/OR1@
Tau turb
B.BBK1OOBR
Fuel/Air ratio, f 2
NonDimensional Parameters
Yes
1@
Value
no
Constant Air/fuel ratio?
Ve/V
inf
JB
B.J
J
Bypass ratioJ1B 1 O / K JB
Vcore/Vinf
VFan/Vinf
Vfan-Vinf/Vcore-Vinf
1.B
Exit Velocities
N Is
p
A
B
B.@
J
J.@
1
1.@
Bypass ratioJ1B 1 O / K JB
Total Thrust
Fan Thrust
Core ThrustNormalized Thrust
f
JOB
B
1B
OB
/B
KB
JBB
J1B
Bypass ratioJ1B 1 O / K JB
Air Fuel Ratio
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MAE 6530 - Propulsion Systems II
Questions??
32