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Design of Supersonic Intake / Nozzle

P M V Subbarao

Associate Professor

Mechanical Engineering DepartmentI I T Delhi

Meeting the Cruising Conditions…

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Design Analysis 121

2* )(

211

12

)(1)(

x M x M A

x A

For a known value of Mach number, it is easy to calculate

area ratio.Throat area sizing is the first step in the design.If we know the details of the resource/requirements, wecan calculate the size of throat.

121

0

0

2

11

1

T

p R A

m

throat

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Cryogenic Rocket Engines

121

0

0

21

1

1

T

p

R A

m

throat

A ratio of LO 2:LH 2 =6:1 T0 = 3300 K.

P0 = 20.4 Mpa

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Specifications of A Rocket Engine

• Specific Impulse is a commonly used measure of performance For Rocket Engines,and for steady state-engine operation is definedAs:

I sp 1

g 0

F thrust •

m propellant

g 0 9.806 m

sec2 (mks)

• At 100% Throttle a RE has the Following performancecharacteristics

Fvacuum = 2298 kNt

Ispvacuum = 450 sec.

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Specific impulse of various propulsion technologies

Engine

"Ve" effective

exhaustvelocity

(m/s, N·s/kg)

Specificimpulse

(s)Energy per kg

(MJ/kg)

Turbofan jet engine 300 3000 43

Solid rocket 2500 250 3.0

Bipropellant liquid rocket 4400 450 9.7

Plasma Rocket 29 000 3000 430

VASIMR 290 000 30 000 43 000

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The Variable Specific Impulse Magnetoplasma Rocket

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Design Procedure

I sp 1 g 0

F thrust •

m propellant

g 0 9.806 msec 2 (mks)

Select a technology : I sp & F thrust

Estimate the mass flow rate of propellent.

121

0

0

21

1

1

T

p R A

m

throat

Carryout heat release or combustion calculations andestimate T0 & p 0

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121

2* )(

21

11

2)(

1)(

x M

x M A x A

Compute properties of gas at each location.

T 0T

1 1

2 M 2

p0 p

T 0T

1 1

1 2

M 2

1

Terminate the design when local static pressure is almost zero.This is exit of the nozzle.Compute Maximum Mach number at the exit.This Mach number will generate the required thrust.

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Plot Flow Properties Along Nozzle Length

• A/A *

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• Mach Number M

^

( j 1) M ^

( j ) F ( M

^

( j ) ) F M

|( j )

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• Temperature T ( x) T 0

1 1

2 M ( x)2

T0 = 3300 KT throat = 2933.3 K

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• Pressure

P0 = 20.4Mpa P throat = 11.32 MPa

P ( x) P 0

1 1

2 M ( x)2

1

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Any Doubts !!!

The maximum number corresponding to an almostzero static pressure of the gas.

This design is meant to work only in Vacuum !!!

What is its performance while launching ???

What is the thrust at sea level ?

Will the nozzle exit flow be a supersonic ?

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SEA Level PerformanceAmbient Pressure is maximum at Sea level.

The design conditions are vacuum.Will the mass flow rate be same ?How to Calculate the corresponding Mass flow rate of

propellant ?

Will p 0 and T 0 remain same ?

What happens if it is not possible to obtain the designmass flow rate ?

One needs to know the Mach number distribution for agiven geometric design!

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Will it satisfy the throat condition?

121

20

0

)(

2

11

)()(

x M

x M x A

T

p R

m

p0 p

T 0

T

1

1 1

2 M 2

1

Find the Maximum Mach number at sea level

Calculate mass flow rate possible at sea level.

12

10

0

21

1

1

T

p R A

m

throat