Design of Supersonic Intake / Nozzle

P M V SubbaraoAssociate Professor

Mechanical Engineering DepartmentI I T Delhi

Meeting the Cruising Conditions…

Design Analysis 12

1

2*

)(2

11

1

2

)(

1)(

xMxMA

xA

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, we can calculate the size of throat.

12

10

0

21

1

1

T

p

RA

m

throat

Cryogenic Rocket Engines

12

10

0

21

1

1

T

p

RA

m

throat

A ratio of LO2:LH2 =6:1

T0 = 3300K.

P0 = 20.4 Mpa

Specifications of A Rocket Engine

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

I sp 1

g0

Fthrust•

m propellant

g0 9.806m

sec2(mks)

• At 100% Throttle a RE has the Following performance characteristics

Fvacuum = 2298 kNt

Ispvacuum = 450 sec.

Specific impulse of various propulsion technologies

Engine

"Ve" effective exhaust velocity

(m/s, N·s/kg)

Specific impulse

(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

The Variable Specific Impulse Magnetoplasma Rocket

Design Procedure

I sp 1

g0

Fthrust•

m propellant

g0 9.806m

sec2(mks)

Select a technology : Isp & Fthrust

Estimate the mass flow rate of propellent.

12

10

0

21

1

1

T

p

RA

m

throat

Carryout heat release or combustion calculations and estimate T0 & p0

12

1

2*

)(2

11

1

2

)(

1)(

xMxMA

xA

Compute properties of gas at each location.

T0

T1

1 2

M 2

p0

p

T0

T

1

1 1

2M 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.

Plot Flow Properties Along Nozzle Length

• A/A*

• Mach NumberM

^

( j1) M^

( j ) F(M

^

( j ) )F

M

|( j )

• Temperature T (x) T0

1 1

2M (x)2

T0 = 3300KTthroat = 2933.3 K

• Pressure

P0 = 20.4Mpa Pthroat = 11.32 MPa

P(x) P0

1 1

2M (x)2

1

Any Doubts !!!

The maximum number corresponding to an almost zero 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 ?

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 p0 and T0 remain same ?

What happens if it is not possible to obtain the design mass flow rate ? One needs to know the Mach number distribution for a given geometric design!

Will it satisfy the throat condition?

12

1

20

0

)(2

11

)()(

xM

xMxA

T

p

Rm

p0

p

T0

T

1

1 1

2M 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

RA

m

throat