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Ideal Turbojet
Parametric Cycle Analysis
© 2015 SIM University. All rights reserved.
• The steps of parametric cycle analysis to an ideal
turbojet
• The output of parametric cycle analysis of an ideal
turbojet
• The differences in performance between ideal
simple turbojet and one with afterburning
© 2015 SIM University. All rights reserved.
Introduction
• Provides thrust even at V0=0 (vs ramjet)
• Turbine extracts only the power required to drive the compressor
and accessories necessary for continuous operation
© 2015 SIM University. All rights reserved.
Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Turbojet
Figure 4-7 T-s Diagram and H-K Diagram of an Ideal Turbojet
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Turbojet
• Input
• Output
- new term (vs ideal ramjet)
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Turbojet
• Equations
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Turbojet
• Equations
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Turbojet
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1700K
Variation of Specific Thrust and TSFC against Mach Number
Source: Soon Kim Tat
Turbojet – Mach Number Variation
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1700K
Variation of Efficiency against Mach Number
Source: Soon Kim Tat
Turbojet – Mach Number Variation
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; πc = 10
Effect of Turbine Inlet Temperature Variation
Source: Soon Kim Tat
Turbojet – Effect of Turbine Inlet Temperature
Variation of Specific Thrust against Compressor Pressure Ratio
Lower
compressor
pressure ratio is
desired at higher
Mach numbers
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1700K
Source: Soon Kim Tat
Turbojet – Compressor Pressure Ratio Variation
Variation of TSFC against Compressor Pressure Ratio
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1700K
Source: Soon Kim Tat
Turbojet – Compressor Pressure Ratio Variation
• Optimum Compressor (for max F/ṁo) Temperature and Pressure Ratio
• Lower compressor pressure ratio is desired for higher Mach number
operation
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Optimum Compressor Pressure Ratio
• Thrust of turbojet being increased by afterburner (after the turbine)
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Afterburning Turbojet
Figure 4-10 T-s and H-K Diagram of an Ideal Afterburning Turbojet
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Afterburning Turbojet
• Input
• Outputc
- new term (vs ideal turbojet)
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Afterburning Turbojet
• Equations
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Afterburning Turbojet
• Equations
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Afterburning Turbojet
• Optimum (max F/ṁo) Compressor Temperature Ratio
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Afterburning Turbojet
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1700K ; Tt4 = 2300K
Variation of Specific Thrust against Compressor Pressure Ratio
Source: Soon Kim Tat
Ideal Afterburning Turbojet
© 2015 SIM University. All rights reserved.
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1700K ; Tt4 = 2300K
Variation of TSFC against Compressor Pressure Ratio
Source: Soon Kim Tat
Ideal Afterburning Turbojet
• Afterburning causes increase in:
– Specific thrust F/ṁ0
– Thrust specific fuel consumption S
• Optimum compressor pressure ratio (maximum F/ṁ0 ):
– Reduces as Mach number increases
– For afterburning turbojet is higher than non-afterburning
→Afterburning turbojet with moderate to high πc still offers high F/ṁ0 at
high flight Mach numbers
• Fuel/air ratio
– In main burner (f )is unchanged
– In afterburner (fAB ) increases with M and πc
– Total (ftot ) decreases with M and is not a function of πc
• Thermal, propulsive, and overall efficiencies are reduced by afterburning
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Comparison of Afterburning
Engine with =30 operates
optimally at M0=2 with AB, and
near optimum at subsonic speeds
where less thrust is required and
S is lower
Optimum Ideal Turbojet
Compressor Pressure
Ratio
Optimum Ideal Turbojet
Performance
© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly
Ideal Turbojet – With and Without Afterburning
• Performing parametric cycle analysis to an ideal
turbojet engines, including with afterburner
• Study of the output of parametric cycle analysis of
an ideal simple turbojet and compare its
performance against one with afterburner.
• Evaluating the optimum compressor pressure
ratio in a turbojet engine.
© 2015 SIM University. All rights reserved.
Summary
• Given an ideal turbojet is operating at the following
conditions:
T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K);
hPR = 42,800 kJ/kg; Tt4 = 1700K
• Compute the optimum compressor pressure ratio
when operating at Mach 1.0. You may use the
following expressions
• Determine the maximum specific thrust of this engine
• You may compare the results with the charts given in
this presentation
© 2015 SIM University. All rights reserved.
Reflection Question