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
Theory of Propulsion 10
Space Transportation System ISRB
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Theory of Propulsion 11
Space Transportation System ISRB Components
Theory of Propulsion 12
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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Theory of Propulsion 13
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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Theory of Propulsion 23
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)
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