MAE 6530 - Propulsion Systems II Homework 5.4 1 A 2 A exit • Engine operates at a free stream Mach number, M ∞ = 0.8. • Cruise Altitude is in the stratosphere, 11 km so T ∞ = 216.65 K. • The design turbine inlet temperature, T 04 = 1944 K • The design compressor ratio, p c = 20 . • Relevant area ratios are A 2 /A * 4 = 10 and A 2 /A 1throat = 1.2 . • Inlet throat area A 1Throat = 20 cm 2 • Assume the compressor, burner and turbine all operate ideally. • Nozzle is of a simple converging type with choked throat, A * 8 =A exit • Stagnation pressure losses due to wall friction in the inlet and nozzle are negligible. à CALCULATE à a) Correct Compressor Massflow and M 2 at compressor face à b) Normalized exit pressure thrust, momentum thrust, and total thrust à c) Velocity ratio across Engine V exit /V ∞ à d) Mach number at diffuser throat, M 1throat à e) Inlet capture area à f) Total Thrust, Isp, TSFC A * 4 f ~ 50
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MAE 6530 - Propulsion Systems II
Homework 5.4
1
A2
Aexit
• Engine operates at a free stream Mach number, M∞ = 0.8. • Cruise Altitude is in the stratosphere, 11 km so T∞ = 216.65 K.• The design turbine inlet temperature, T04 = 1944 K • The design compressor ratio, pc = 20 . • Relevant area ratios are A2 /A*
4 = 10 and A2/A1throat = 1.2 . • Inlet throat area A1Throat = 20 cm2
• Assume the compressor, burner and turbine all operate ideally. • Nozzle is of a simple converging type with choked throat, A*
8=Aexit• Stagnation pressure losses due to wall friction in the inlet and nozzle are negligible. à CALCULATEà a) Correct Compressor Massflow and M2 at compressor faceà b) Normalized exit pressure thrust, momentum thrust, and total thrustà c) Velocity ratio across Engine Vexit/V∞à d) Mach number at diffuser throat, M1throatà e) Inlet capture areaà f) Total Thrust, Isp, TSFC
A*4
f~ 50
Stephen Whitmore
• Calculate Associated Fuel Enthalpy
MAE 6530 - Propulsion Systems II
Homework 5.4 (2)
1
A2
Aexit
• Now allow an expandable Nozzle where, Aexit > A*8
à CALCULATEà a) Optimal expansion ratio for nozzle Aexit /A*
8à b) c) Velocity ratio across Engine Vexit/V∞à c) thrust, Isp, TSFC of optimal nozzle, à d) Assuming the same combustor temperature and inlet throat area as previous page
à At what compressor demand pc does the inlet throat choke ( @ A1throat )
à Plot the Compressor operating line à pc vs corrected massflow, f(M2) for 1 < pc < pc @ choke
à Plot the capture area A∞ vs corrected massflow, f(M2) for 1 < pc < pc @ choke
A*4
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION
1
A2
Aexit
A*4
Stephen Whitmore
MJ/kg
Stephen Whitmore
70.735
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION (2)
1
A2
Aexit
à CALCULATEà a) Corrected Compressor massflow and M2 at compressor face
à b) Normalized exit pressure thrust, momentum thrust, and total thrust
à c) Velocity ratio across Engine Vexit/V∞
A*4
f +1f≈1
à d) Mach number at diffuser throat, M1throat
à e) Inlet capture area
Sonic Exit THRUST DATA
f~ 50
Fuel− to− Airflow_ Matching1f=τλ−τr ⋅τcτ f −τλ
Solve for τ f
→hfcp ⋅T∞
= τ f = τλ+ f ⋅ τλ−τr ⋅τc( )
Solve for hf→ hf = cp ⋅T∞ ⋅ τλ+ f ⋅ τλ−τr ⋅τc( )⎡
⎣⎢⎤⎦⎥=
1004.96J /kg−K ⋅216.65K ⋅ 8.973+50 ⋅ 9.973−1.128⋅2.25355( )⎡⎣⎢
⎤⎦⎥=
70.735MJ /kg
Stephen Whitmore
Calculate Fuel Enthalpy
Stephen Whitmore
Wow! hot stuff!
Stephen Whitmore
MJ/kg
Stephen Whitmore
70.735
Stephen Whitmore
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION (2)
1
A2
Aexit
à CALCULATEà a) Corrected Compressor massflow and M2 at compressor face
à b) Normalized exit pressure thrust, momentum thrust, and total thrust
à c) Velocity ratio across Engine Vexit/V∞
A*4
f +1f≈1
à d) Mach number at diffuser throat, M1throat
à e) Inlet capture area
Sonic Exit THRUST DATA
f~∞
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION (3)
1
A2
Aexit
A*4
• Now allow an expandable Nozzle where, Aexit > A*8
à CALCULATEà a) Optimal expansion ratio for nozzle Aexit /A*
8
à b) c) Velocity ratio across Engine Vexit/V∞
à c) thrust of optimal nozzle
à
OPTIMAL THRUST DATA
à
f~ 50
Stephen Whitmore
MJ/kg
Stephen Whitmore
70.735
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION (4)à d) Assuming the same combustor temperature and inlet throat area
à Plot the Compressor operating line à pc vs corrected massflow for 1 < pc < Chokeà Plot the capture area A∞ vs corrected massflow for 1 < pc < Choke
Stephen Whitmore
Stephen Whitmore
Stephen Whitmore
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION (4)à d) Assuming the same combustor temperature and inlet throat area
à Plot the Compressor operating line à pc vs corrected massflow for 1 < pc < Chokeà Plot the capture area A∞ vs corrected massflow for 1 < pc < Choke
MAE 6530 - Propulsion Systems II
Homework 5.4, SOLUTION (4)à d) Assuming the same combustor temperature and inlet throat area
à Plot the Compressor operating line à pc vs corrected massflow for 1 < pc < Chokeà Plot the capture area A∞ vs corrected massflow for 1 < pc < Choke
MAE 6530 - Propulsion Systems II 10
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