chapt 12 solid rockets(1)

8/11/2019 Chapt 12 Solid Rockets(1)

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Solid Propellant Rockets

MAE 4930/7930 Aerospace Propulsion

Prof. Craig A. Kluever

University of Missouri-Columbia

Mechanical & Aerospace Engineering

Solid Propellant Rockets

Solid rocket motors (SRMs) consist of a pressure vessel

filled with a solid mixture of oxidizer and fuel

Obviously no need for external storage tanks, feed systems,

pumps, etc

Solid rockets are relatively simple (compared to liquid

propellant rockets) and reliable

Applications of solid rocket motors: Military

Sounding rockets

Space boosters


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Solid Rocket Motors (SRMs)

Advantages of solid propellant rockets

Simplicity: no moving parts, no injection system, no need to fill

with propellants before launch

Storage, handling, and service is much easier compared to

liquid-propellant rockets

Highly reliable (no moving parts!)

Payload mass ratio is high (lack of massive subsystems)

Overall cost is low compared to liquid rockets

Solid Rocket Motors (SRMs)

Disadvantages of solid propellant rockets

Because propellant mixture must be cast as a single piece,

there are limitations in the size of a block. Therefore, clusters

of smaller SRMs are often used

Performance is lower than liquid-propellant rocket (lower Isp)

Cannot turn off the thrust (unlike liquid rocket)

Burn duration is relatively short, so total impulse is limited

No means to cool nozzle compared to liquid-propellant rockets,

which circulate liquid propellant through nozzle jackets

Performance of solid propellant is sensitive to temperature, sothe associated manufacturing process is costly and difficult


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Solid Propellant Rockets:Characteristic Features

Solid Rocket Motor (SRM) sizes can range from lbfthrust to 2.5 million lbf thrust (Shuttle SRB)

The thrust profile can be ~constant, increase, or

decrease with time (due to grain cross-section)

The SRM has four components:

Combustion chamber: stores and contains propellant during

high-pressure burning

Igniter

Solid propellant (is burned for hot gases)

Nozzle (expands gas to high velocity)

Theory of Propulsion 6

Motor casing

Igniter

Burning surface

Solid propellant

Throat

Nozzle

Combustion chamber

Schematic diagram of solid rocket motor components


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SRM Combustion Chamber

The combustion chamber is the mechanical casing

which is normally a thin-walled cylindrical pressure

vessel

Aluminum, fiber-reinforced plastic, titanium

Walls must withstand stresses from

Pressure load during combustion

Thermal stresses from high-temperature combustion

Dynamic loads during launch

Staging loads

SRM Construction/Igniter

O-rings are used as pressure seals between motor

segments

The igniter is located at the front end, and are either

pyrotechnic or pyrogen igniters

Pyrotechnic: explosives or high-energy chemical

combinations (boron + potassium perchlorate) activated

by electric current through a squib

Pyrogen: small rocket motors that start the larger SRM;

initiated by a pyrotechnic device


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Solid Rocket Propellants

Three categories for solid propellants:

Double-base or homogeneous propellant: chemical molecule

contains both fuel and oxidizer. An example is nitroglycerin +

nitrocellulose (highly explosive). Characteristics include low

combustion temperature, low Isp (190-230 s), and almost

smokeless exhaust gases

Composite or heterogeneous propellant: crystalline oxidizer

(e.g., ammonium perchlorate) + powdered fuel (e.g., aluminum)

in a hydrocarbon binder (Shuttle SRB). This putty-like mixture is

easily cast into any shape and cured between 100-180 deg F.

Less hazardous to handle. Isp is 230-265 sec

Composite double-based propellant: combination of the two

types described above


Space Transportation System ISRB


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Space Transportation System ISRB Components


Ammonium perchlorate (NH4ClO4) 70%

Polybutadiene acrylonitrile (PBAN) 14%

Aluminum powder 16%

Iron oxidizer powder 0.07% (catalyst)

Propellant mass fraction = 88%

Ammonium perchlorate produces HCl in the combustion

products and forms a white cloud when exhauseted into even

mildly humid air.

PBAN is a polymeric rubber-based binder that also serves as

fuel

Aluminum is added to enhance thrust (HV = 32 MJ/kg)

Space Shuttle SRB propellant composition


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SRB

Thrust(lbs)

Mission elapsed time (sec)

2 million lbs

3 million lbs

100 sec

Space Transportation System ISRB Performance

Burning of Propellants Once propellant is ignited, burning takes place perpendicular to

surface, and subsequent regression of burning surface is in parallel

layers

Rate of regression of the burning surface is the burning rate, r,

characterized by the empirical relation

Variablepc is the combustion chamber pressure

Variable a is a function of propellant composition and temperature

(ranges from 0.002 to 0.08 when ris in inch/s andpc in psia)

Exponent n (combustion index) is independent of temperature

n

capr= inch/s or mm/s


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Burning of Propellants (2)

Chamber pressure pc is determined by the equilibrium that shouldexists between gas generation rate (combustion) and nozzle

exhaust flow rate

Therefore, we can equate mass-flow rate at burning surface (gas

generation) and mass-flow of hot gas out the nozzle

The mass-rate generated by burning is

Mass flow-rate of hot gas out the choked nozzle is

n

cbpbp apArAm ==&

*c

Ap

RTApm tc

c

tc =

=&

whereAb = combustion surface area

p = propellant density

Burning of Propellants (3) Equate the two expressions for mass flow rate, and solve for area

ratio

Solving for chamber pressure

cp

n

c

t

b

RTa

p

A

A =

1

n

t

b

n

t

bcp

cA

AC

A

ARTap

=

=

1

11

1

where C= constant for a given propellant


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Stable Burn and Mass Flow Rate

Mass-

flow

rate

Nozzle dm/dt

(choked flow)

Chamber pressure,pc

Stable

equilibrium

Gas generation dm/dt

(burn surface)

Combustion index 0 < n < 1

n

cbp apAm =&

high pressure

flow becomes unchoked, and

pc drops back to stable point

low

pressure

Low pressure: gas generation rate > nozzle flow rate, so

chamber pressure increases to stable point

c

tcRT

Apm

=&

Unstable Burn and Mass Flow Rate

Mass-

flow

rate

Nozzle dm/dt

(choked flow)

Chamber pressure,pc

Unstable

equilibrium

Gas generation dm/dt

(burn surface)

Combustion index n > 1

n

cbp apAm =&

high pressure

more hot gas is generated than nozzle

can accommodate, leading to explosionlow

pressure

Low pressure: gas generation rate < nozzle flow rate, so chamber pressure

continues to decrease (no restoring mechanism), eventually

leading to flame out

c

tcRT

Apm

=&


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Burning of Propellants (4)

The previous slides show that for a stable burn, we require that thecombustion index 0 < n < 1

In addition, n should be as small as possible

For example, if n = 0.7 and a crack in the propellant develops so

that the surface burn area increases by 20%, then we have

1/(1 -n) = 3.333 and chamber pressure rise is

If n = 0.2, then 1/(1 n ) = 1.25, so pressure rise is 1.21.25 = 1.26

84.12.1 333.3333.3

1

1

=

=

=

t

bn

t

bc

A

AC

A

ACp High stress

(manageable stress)

Propellant Surface Geometry The gas-generation mass rate is not necessarily constant, but

depends on the surface burn area,Ab, and burn-rate r

Of course, thrust profile depends on nozzle mass-flow rate

Three schemes for shaping the thrust profile:

Progressive burning: burn area, pc, and thrust increase with time Neutral burning: burn area, pc, and thrust remain constant

Regressive burning: burn area, pc , and thrust decrease with time

n

cbp apAm =&

n

cbpsp apAIgT 0=


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Propellant Surface Geometry (2)

Burn time

Thrust

Neutral End-burning

ProgressiveCylindrical burning

Regressive

Rod burning

Early SRMs used

end burning or

cigarette burning

Propellant of density p Propellant burning areaAb

Surface recession rate r

Combustion chamber volume c(t)

Throat areaAt

Combustion chamber volume varies with time

An end-burning grain is shown for illustration

End-burning has problems with dramatic c.g. shift during burn


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Star grain Cylindrical

grain

End-burning

grain

Propellant grain configurations

Cruciform

grain

STS ISRM has 11-pointed star

transitioning into cylindrical grain

Propellant Surface Geometry (3) Tube-type burning (cylindrical burn) is a simple method for

progressive burning, where burn areaAb and thrust increase with

time

Main disadvantage: initial burn surface may be too small and final

surface too large (final thrust is excessive)

Cruciform or rod-type burning are regressive: burn area decreases

with time

Can be used to limit acceleration of rocket


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Web Fraction

Propellant grain selection and design depends on two importantgeometric parameters:

Web fraction, wf Volumetric loading, VL

Web fraction: ratio of propellant web to grain outer radius

Web: minimum thickness of grain from the ignition surface to case wall

D

dDwf

=Web fraction

D

d

D

rtw burnf

2=or

r= burning rate, mm/s or in/s

Volumetric Loading Volumetric loading, VL: fraction of total available combustion

chamber volume Va occupied by the propellant Vp

a

p

LV

VV =Volumetric loading

0.70.1 0.25Wagon wheel

0.75 0.90.3 0.4Starwf( 2 wf)0.7 0.8Internal burning

11End burning

VLwfConfiguration


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SRM Design

Start with specifications for thrust, burn time, and nature of mission

Select a propellant based on experience, heritage, etc

From propellant, estimate chamber pressure pc and temperature Tc From propellant, estimate and compute c*

Compute burning rate rfrom propellant (function of pc)

Select a grain profile

Compute thrust coefficient cF and expansion ratioAe /At

Compute Isp = cFc*/g0

SRM Design (2) Compute propellant weight Wp = Ttburn / Isp

Compute propellant volume: Vp = Wp / p

Compute throat area:At = T / cF pc

Compute burning areaAb fromAt , pc , a, p

Assuming constantAb , compute web thickness = rtburn

Compute geometric dimensions (case diameter D, length L) from

web fraction and volumetric loading (previous table)

chapt 12 solid rockets(1)

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