rocket .ppt

7/29/2019 rocket .ppt

1/35

Analysis of Rocket Propulsion

P M V Subbarao

Professor

Mechanical Engineering Department

Continuously accelerating Control Volume.


2/35

THE TSIOLKOVSKY ROCKET EQUATION


3/35

Force Balance on A Rocket

DgMT

dt

dVM r

rr sin

DgM

dt

dMC

dt

dVM r

rrr sin


4/35

r

r

r

r

M

Dg

dt

dM

M

C

dt

dV sin

Let

dragrnalgravitatiorspacerrVVVV


5/35

bt

nalgravitatiordtgV

0

sin bt

rdragr

dtM

DV

0

bt

e

rir

r

spacer Mr

MCdt

dt

dM

M

CV

0

ln

For a typical launch vehicle headed to an orbit, aerodynamic

drag losses are typically quite small, on the order of 100 to

500 m/sec.

Gravitational losses are larger, generally ranging from 700 to1200 m/sec depending on the shape of the trajectory to orbit.

By far the largest term is the equation for the space velocity

increment.


6/35

REACHING ORBIT

The lowest altitude where a stable orbit can be maintained, is atan altitude of 185 km.

This requires an Orbital velocity approximately 7777 m/sec.

To reach this velocity from a Space Center, a rocket requires an

ideal velocity increment of 9050 m/sec.

The velocity due to the rotation of the Earth is approximately

427 m/sec, assuming gravitational plus drag losses of 1700

m/sec.

A Hydrogen-Oxygen system with an effective average exhaustvelocity (from sealevel to vacuum) of 4000 m/sec would require

Mi/ Mf= 9.7.


7/35

Geostationary orbit

A circular geosynchronous orbit in the plane of the Earth's

equator has a radius of approximately 42,164 km (26,199

mi) from the center of the Earth.

A satellite in such an orbit is at an altitude of

approximately 35,786 km (22,236 mi) above mean sea

level.

It maintains the same position relative to the Earth's

surface.

If one could see a satellite in geostationary orbit, it would

appear to hover at the same point in the sky.

Orbital velocity is 11,066 km/hr= 3.07 km/sec (6,876

miles/hr).


8/35

Travel Cycle of Modern Spacecrafts


9/35

MULTISTAGE ROCKETS

With current technology and fuels, a single stage rocket toorbit is still not possible.

It is necessary to reach orbit using a multistage system

where a certain fraction of the vehicle mass is dropped off

after use thus allowing the non-payload mass carried toorbit to be as small as possible.

The final velocity of an n stage launch system is the sum of

the velocity gains from each stage.

nn VVVVV ...........321


10/35

ANALYSIS OF MULTISTAGE ROCKETS

M0i : The total initial mass of the ith stage prior to

firing including the payload mass,ie, the mass of

i, i+1, i+2, i+3,...., n stages.

Mpi: The mass of propellant in the ith stage.


11/35

Msi : Structural mass of the ith stage alone including the mass of its

engine, controllers and instrumentation as well as any residual

propellant which is not expended by the end of the burn.

ML : The payload mass

Mass ratio

pii

i

i

ii

MM

M

M

MR

0

0

10

0

sii

sipii

iMM

MMMR

10

10

1,

lni

ri

ispacer Mr

MCV


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100

10

100

10

ii

sii

ii

sipii

i

MMMM

MM

MMM

R

100100

10

100

101

ii

si

ii

i

ii

i

i

MMMMMM

MMM

R


13/35

Structural coefficient

pisi

si

ii

sii

MM

M

MM

M

100

Payload ratio

100

10

ii

i

iMM

M

Ln

L

nn

n

nMM

M

MM

M

0100

10


14/35

ii

iiR

1

Space (Ideal) velocity increment

n

iinRCV

1

ln

Payload fraction

n

LL

M

M

M

M

M

M

M

M

M

M

003

04

02

03

01

02

01

....


15/35

nnL

M

M

1....1113

3

2

2

1

1

01


16/35

MOMENTUM BALANCE FOR A ROCKET

Rocket mass X Acceleration = Thrust Drag -gravity effect

dragTr

r FgF

dt

dVM sin


17/35

EFFECTIVE EXHAUST VELOCITY

The total mechanical impulse (total change of omentum)

generated by an applied force, FT, is:

riV

i

dragr

r

ti

Tii dtFgdt

dVMFI00

sin

The total propellant mass expended is

ti

ipi dtmM

0


18/35

The instantaneous change of momentum per unit expenditure

of propellant mass defines the effective exhaust velocity.

ii

Ti

pi

i

i Sm

F

dM

dI

C


19/35

Rocket Principles

High pressure/temperature/velocity exhaust gases

provided through combustion and expansion through

nozzle of suitable fuel and oxidiser mixture.

A rocket carries both the fuel and oxidiser onboard

the vehicle whereas an air-breatherengine takes in

its oxygen supply from the atmosphere.


20/35

Criteria of Performance

Specific to rockets only. thrust

specific impulse

total impulse

effective exhaust velocity

thrust coefficient

characteristic velocity


21/35

Thrust (F)

For a rocket engine:

m

ambeeejectsejectsT ppAUmF

Where:

= propellant mass flow rate

pe = exit pressure, paamb = ambientpressure

Uejects = exit plane velocity, Ae = exit area


22/35

Specific Impulse (I or Isp)

The ratio of thrust / ejects mass flow rate is used to define arockets specific impulse-best measure of overall performance of

rocket motor.

In SI terms, the units of I are m/s or Ns/kg.

In the US:

with units of seconds - multiply by g (i.e. 9.80665 m/s2) in

order to obtain SI units of m/s or Ns/kg.

Losses mean typical values are 92% to 98% of ideal values.

ejects

T

m

F

spI


23/35

Total Impulse (Itot)

Defined as:

where tb = time of burning

If FT is constant during burn:

bt

TdtF0

totalI

bT tF totalI


24/35

Thus the same total impulse may be obtained byeither :

high FT, short tb (usually preferable), or

low FT, long tb

Also, for constant propellant consumption (ejects) rate:

bejects

ejects

T tmm

F

totalI


25/35

Effective Exhaust Velocity (c)

Convenient to define an effective exhaustvelocity (c), where:

cmF ejectsT

I

ejects

T

m

Fc

ejects

e

mpc

eambe

ApU


26/35

Thrust Coefficient (CF)

Defined as:

t

TF

A

FC

cP

where pc = combustion chamber pressure,

At = nozzle throat area

Depends primarily on (pc/pa) so a good indicator of

nozzleperformance dominated by pressure ratio.


27/35

Characteristic Velocity (c*)

Defined as:

(6)ejects

t*

m

AC

cP

Calculated from standard test data.

It is independent of nozzle performance and is

therefore used as a measure ofcombustion

efficiency dominated by Tc (combustion chamber

temperature).


28/35

Thermodynamic Performance - Thrust

Parameters affecting thrust are primarily: mass flow rate

exhaust velocity

exhaust pressure nozzle exit area
http://www.fas.org/man/dod-101/sys/missile/agm-119-980721-N-5961C-001.jpg


29/35

Thermodynamic Performance- Specific Impulse


30/35

Thermodynamic Performance

- Specific Impulse

Variable Parameters - Observations

Strong pressure ratio effect - but rapidly diminishing returns

after about 30:1.

High Tc value desirable for high I - but gives problems with

heat transfer into case walls and dissociation of combustion

products practical limit between about 2750 and 3500 K,

depending on propellant.

Low value of molecular weight desirable

favouring use ofhydrogen-based fuels.

Low values of desirable.


31/35

31

Thrust Coefficient (CF) Maximum thrust when exhausting into a

vacuum (e.g. in space), when: (11a

)


32/35

Thrust Coefficient (CF)

- Observations

More desirable to run a rocket under-expanded

(to left of optimum line) rather than over-expanded.

Uses shorter nozzle with reduced weight and size.

Increasing pressure ratio improves performance

but improvements diminish above about 30/1.

Large nozzle exit area required at high pressureratios implications for space applications.


33/35

Actual Rocket Performance

Performance may be affected by any of the followingdeviations to simplifying assumptions:

Properties of products of combustion vary with static

temperature and thus position in nozzle.

Specific heats of combustion products vary with temperature. Non-isentropic flow in nozzle.

Heat loss to case and nozzle walls.

Pressure drop in combustion chamber due to heat release.

Power required for pumping liquid propellants.

Suspended particles present in exhaust gas.


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Internal Ballistics

Liquid propellant engines store fuel and oxidiserseparately - then introduced into combustion chamber.

Solid propellant motors use propellant mixture

containing all material required for combustion.

Majority of modern GW use solid propellant rocket

motors, mainly due to simplicity and storage

advantages.

Internal ballisticsis study of combustion process of

solid propellant.


35/35

Solid Propellant Combustion

Combustion chamber is high pressure tankcontaining propellant charge at whosesurface burning occurs.

No arrangement made for its control chargeignited and left to itself so must self-regulateto avoid explosion.

Certain measure of control provided bycharge and combustion chamber design andwith inhibitor coatings.

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rocket .ppt