homework 6 - utah state university

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

Stephen Whitmore


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


fan3

Bypass


Fan

Bypass Exhaust

fan3

Fan


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


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


fan3

Bypass


Fan

Bypass Exhaust

fan3

Fan


core4

core5

coreexit

fanexit

fanexit

∞

1

2

T= Fthrustp∞ ⋅ A∞

I=Isp ⋅g0c∞

TSFC= 1g0 ⋅ Isp

turbofan_cycle_..0_solution.vi/Users/stephenwhitmore/Desktop/MAE .@AB/MAE_.@AB_Web/New_Course/Section./turbofan_cycle_..0_solution.vi

Last modified on I0/J/0B at IBKAL AMPrinted on I0/J/0B at IBKN@ AM

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

[email protected]

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

[email protected]@

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

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


JDDM.R0

Cp, J/kg-K

J.M

Gamma

JKDD


0


2

Fan Pressure Ratio

JD.J0

Bypass ratio

D.CB



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


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

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

Last modified on J1///1B at KLBK PMPrinted on J1/N/1B at JBLOO AM

Page J

B.N

Mach Number

/

Altitude, km

O.1/KE+N


JBBO.R/

Cp, J/kg-K

J.O

Gamma

JNBB


/


1

Fan Pressure Ratio

B.A@



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


/.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


Vcore/Vinf

VFan/Vinf

Vfan-Vinf/Vcore-Vinf

1.B

Exit Velocities

N Is

p

A

B

B.@

J

J.@

1

1.@


Total Thrust

Fan Thrust

Core ThrustNormalized Thrust

f

JOB

B

1B

OB

/B

KB

JBB

J1B


Air Fuel Ratio


Questions??

32

homework 6 - utah state university

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