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Ideal Ramjet Parametric Cycle Analysis

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Introduction

• The steps of parametric cycle analysis to an ideal ramjet

• The output of parametric cycle analysis of an ideal ramjet

© 2015 SIM University. All rights reserved.

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• Brayton Cycle Engine with no rotating part

• Compression of air accomplished by forward motion only

© 2015 SIM University. All rights reserved.

Source: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly

Ideal Ramjet

Figure 4-3 T-s Diagram and H-K Diagram of an Ideal Ramjet(adapted from R-1, page 267)

© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly

Ideal Ramjet

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• Input

• Output

• Example: – T0 = 220 K– γ = 1.4– cP=1.004 kJ/(kg K)– hPR = 42,800 kJ/kg– Tt4 = 1600, 1900, and 2200K

t4

© 2015 SIM University. All rights reserved.

Ideal Ramjet

• Equations:

At V0 = 0, Ƭr = 1,and V9/a0, F/ṁ0 = 0

© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly

Ideal Ramjet

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At V0 = 0, Ƭr = 1Thus ηT , ηO= 0

=ℎ

−

=̇⁄

= 1 −1

=2⁄ + 1

= =2 − 1

+

• Equations

© 2015 SIM University. All rights reserved. Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly

Ideal Ramjet

© 2015 SIM University. All rights reserved.

Source: Soon Kim Tat

T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1600, 1900, and 2200K

Variation of Specific Thrust and TSFC against Mach Number

Varying M0 in Ideal Ramjet

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• Optimum Mach Number (max F/ṁo)

• Occurring when

© 2015 SIM University. All rights reserved.

Max Specific Thrust in Ideal Ramjet

© 2015 SIM University. All rights reserved.Source: Soon Kim Tat

T0 = 220 K; γ = 1.4; cP=1.004 kJ/(kg K); hPR = 42,800 kJ/kg; Tt4 = 1900K

Variation of Efficiencies against Mach Number

Varying M0 in Ideal Ramjet

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Figure 4-5 Ideal Ramjet Thrust per Unit Area vs Mach Number

M0~2.3 (opt)

M0~5.3

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M2 = 0.5; Altitude = 12 km; Tt4 = 1900K; d = 1.0

Adapted: “Elements of Propulsion: Gas Turbines and Rockets” by Jack D. Mattingly

Mass Flow of Ideal Ramjet

• Performing parametric cycle analysis to an ideal ramjet– Effects on thrust and fuel consumption

• Study of the output of parametric cycle analysis of an ideal ramjet– Varying Mach number– Varying combustor exit temperature

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Summary

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• Using relationship for speed of sound, for an ideal ramjet, show that

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Reflection Question