AE 8129 Rocket Propulsion
Introduction
Solid-Propellant Rocket Motors
Liquid-Propellant Rocket Engines
Hybrid Rocket Engines
Air-Breathing Rocket Engines
Non-Chemical Space Propulsion
Systems
Delta II Launch Vehicle
Introduction to Solid-Propellant
Rocket Motors (SRMs)
• Simplest of the chemical rockets (lack of
moving parts or plumbing)
• Motor is ignited, and passively allowed to
burn to completion; thrust profile with time
will be set by the propellant charge’s shape
and pre-determined burning characteristics
• Competitive for one-burn-only applications
• Thrust range: milli-newtons (micro-thruster)
to mega-newtons (launch vehicle booster)
Space Shuttle SRB (note that the motor is
assembled from 4 motor case and propellant
segments as shown, due to the large size)
SRM Design Considerations
• Propellant grain (charge) can be bonded,
loaded or cast into the motor
chamber/casing
• Propellant must have its surface
temperature raised above its auto-ign. temp.
to allow for combustion to proceed
• Pressure-time and corresponding thrusttime profile will depend on the grain shape
Cutaway diagram of an ATK Thiokol Orion 32 solid rocket motor. This
3-m long SRM produces a mean thrust of around 29000 lbf (129 kN) over
a burn time of around 40 seconds. Observe the submerged nozzle design
(nozzle convergence is substantially within the chamber boundaries; allows
shorter overall motor length). Igniter is shown in the central port at the head
end of the motor (left side in above diagram).
SHAPE OF PROPELLANT GRAINS QUENCHED
AT DIFFERENT TIMES
Start condition
Quenched at 1.5 s
Various thrust profiles that can result from differing propellant grain
designs. Star or wagon-wheel grains (at right) produce a roughly neutral
profile for a good portion of the firing.
Quenched at 2.5 s
Single-stage sounding rocket employing BATES segmented-cylinder
motor; segmented grain produces a neutral thrust profile. Without the
segmentation, one would have a progressive thrust profile.
Finocyl propellant grain design (fins + cylinder). This design will produce a relatively
neutral thrust profile.
Slotted propellant grain design . This design will produce a
regressive thrust profile.
SRM Design Considerations
Ignition can by various means; variants of the jet igniter
below are quite popular for motors of all sizes
Pelleted (basket) igniter used for igniting tactical
missile solid rocket motor.
Pyrogen jet igniter used for igniting tactical
missile solid rocket motor.
SRM Design Considerations
• Solid propellant categories: composite
(heterogeneous), double-base
(homogeneous), hybrid (crossovers
between heterogeneous and homogeneous)
• Example common composite propellant:
AP/HTPB/Al/Fe2O3
ammonium perchlorate (oxidizer/solid crystal), 75%
aluminum (fuel/stabilizer/powder), 8%
hydroxyl-terminated polybutadiene (fuel/polymeric binder), 15%
ferric oxide (catalyst/powder), 2%
Combustion Processes
Thermal decompostion (endothermic process: requires
heat input to system) of AP, example products of reaction for
balanced equilibrium concentrations:
2NH4ClO4(solid) + heat  2O2(gas) + N2(g) + 4H2O(g) + Cl2 (g)
In practice, decomposition products would also include
transitional and equilibrium quantities of HClO4 , NH3 , CO2 ,
OH , CO , HCl , H2 , etc.
Thermal decomposition of HTPB may be approximated via:
HO(C4H4)50OH(s) + heat  49C4H4(g) + 2CO(g) + C2H6(g)
Combustion Processes (cont’d)
Combustion of HTPB decomposition products with surrounding
hot gas, with exothermic heat release and example products
of reaction for balanced equilibrium concentrations:
C4H4(g) + 5O2(g)  4CO2 (g) + 2H2O (g) + heat
As per the previous slide, O2 as a reactant provided from the
decomposition of AP.
Combustion Processes (cont’d)
Combustion of aluminum with surrounding hot gas, example
products of reaction for balanced equilibrium concentrations:
4Al(s) + 3O2(g)  2Al2O3 (s) + heat
2Al(s) + 3Cl2(g)  2AlCl3 (g) + heat
Assuming a general reaction process with exothermic heat
output, for AP and aluminum as reactants:
6NH4ClO4(s) + 10Al(s)  4Al2O3(s) + 2AlCl3(g) + 3N2(g)
+ 12H2O + heat
Double-Base Propellants
• Example double-base propellant:
NC/NG/MgO
nitrocellulose (fuel/oxidizer, solid), 75%
magnesium oxide (stabilizer/powder), 3%
nitroglycerine (fuel/oxidizer, liquid before absorption by NC), 22%
Hybrid/Crossovers
• Composite-modified double-base
propellants the most common hybrid
between the traditional categories
• To add energy to a composite propellant,
one occasionally sees the use of highenergy RDX, HMX, etc., homogeneous
compounds at some loading percentage
Solid-Propellant Burning Rate Models
• Solid propellants burn under different
driving mechanisms
• Under pressure, one can use de
St. Robert’s law:
rb / r o
1.5
rp  Cp
n
1.0
1e+7
2e+7
p (Pa)
• Influence of outside temperature on C:
C  C o exp[ p ( Ti  Tio )]
, lower
Ti , lower C
Pressure-dependent burning rate behaviour of three propellant categories.
Plateau and mesa burning characteristics are observed less often in the typical
operational pressure ranges for solid rockets.
• Solid propellant auto-ignition temperature:
Qs
Tas  Ti 
Cs
• For net near-surface heat release:
m Al
m AP
m HTPB
Qs 
 Qs ,AP 
 Qs ,HTPB 
 Qs ,Al
mp
mp
mp


0.75(+1,045,000) + 0.15(-1,813,000) + 0.10(-280,000)
+483,800 J/kg
m Al
m AP
mHTPB
Cs 
 C s ,AP 
 C s ,HTPB 
 C s ,Al
mp
mp
mp


Tas  294 
0.75(1420) + 0.15(2100) + 0.10(900)
1470 J/kgK
483800
 623 K, auto-ign. temp.
1470
1
TS  Tas 
2 p
,
burning surface temperature
1
TS  623 
= 935 K
2( 0.0016 )
Erosive Burning
• Under core gas flow, solid propellant is
observed to be burning as a function of
axial mass flux (G = u ). Lenoir and
Robillard derived a convective heat
feedback model:
rb  ro  re  Cp  G d p
n
0.8
0.0288C p  0.2 Pr 2 / 3 ( TF  TS )

 s Cs
( TS  Ti )
0.2
exp( rb  s / G )
,  = 53
• Port diameter term was included later, when results
showed x-dependence not valid in longer motors. It
wasn’t long until equation for  was abandoned, and
both  and  were wide-ranging correction
coefficients, depending on motor. Negative erosive
burning ignored.
• In 2007, Greatrix introduced a less empirical model with
the influence of several parameters now explicitly
included, so as to model both negative and positive
erosive burning more effectively:
rb
rb 
ro
r
neg.
 ro  re
pos.
Burning Augmentation
1.5
1.0
Theory
Expt.
0.5
0
2000
4000
6000
Mass Flux, kg/m2-s
Theoretical and experimental (Godon et al (1987)) data for burning rate
augmentation as a function of mass flux, double-base propellant A (Greatrix (2007)).
Initial dip in burning rate below base level due to negative erosive burnng, with
recovery later as positive erosive burning becomes dominant at higher G values
• Positive erosive burning determined via
convective heat feedback premise:
h( TF  TS )
re 
 s [ C s ( TS  Ti )  H s ]
h
C p s
Pr 2 / 3 u 
 s  u ( f / 8 )
2

, positive e.b.
, Reynolds’ analogy
, surface shear stress
h* 
( f *)
1 / 2
k 2 / 3C p
1/ 3
 2/3
Gf *
8
, zero-transpiration h
 / dp
2.51
 2log 10 [

]
1/ 2
3.7
Re d ( f *)
h
exp (
 s rb C p
 s rb C p
h*
) 1
, zero-transpiration f
, transpiration correction
• Negative erosive burning attributed to
laminar stretching of the effective reaction
distance of the combustion zone at low
axial flow speeds
rb
rb 
ro
rb
ro
1
 cos[ tan (
r
vf
 ro  re
, overall
)]  cos[ tan ( K   o [1  ( f / f lim )
1
1/ 2
u 
]
)]
 s ro
, incorporates stretching effect on lowering
the base burning rate, for f < flim = 2.5x10-4,
and K = 2600 m-1
1.5
Burning Augmentation
u eff
r
1.0
Theory
Expt.
0.5
0
2000
4000
6000
 s rb
8 s rb
f 8
/( exp[
]  1)
G
G( f *)
2
Mass Flux, kg/m -s
C p ( TF  TS )
k
o 
 n [ 1 
]
 s ro C p
C s ( TS  Ti )  H s
, transpiration
correction on
friction factor
, reference combustion zone
thickness
Burning under Acceleration
• Under normal acceleration, solid
propellant is observed to be burning as a
function of an ; consider Greatrix [1994]
model:
rb  [
C p ( TF  TS )
C s ( TS  Ti )  H s
]
( rb  Ga /  s )
exp[ C p  o (  s rb  Ga ) / k ]  1
C p ( TF  TS )
k
o 
 n [ 1 
]
 s ro C p
C s ( TS  Ti )  H s
, ref. combustion zone thickness
Accelerative mass flux:
an p  o ro
2
Ga  {
} 0 cos d
rb RT F rb
Augmented displacement angle:
ro 3
d  tan [ K ( ) tan ]
rb
1
Acceleration vector orientation angle:
a
  tan ( )
an
1
K=8
Burning Augmentation
5
4
3
2
1
0
5000
10000
15000
Normal Acceleration, g
Predicted burning rate augmentation of example composite propellant due to
normal acceleration.
Burning Augmentation
1.5
1.0
0
10
20
30
Orientation Angle, deg
Predicted burning rate augmentation reduction as a function of
acceleration orientation angle  , for an of 500 g acting on example
composite propellant.
Internal Ballistic Analyses for Steady & Nonsteady Operation of SRMs
• Internal ballistic analysis: combined
modelling of internal flow and combustion
• Consider simpler case, when low flow
speed in combustion chamber (upstream
of the nozzle) is assumed:
.
m in   s Srb 
 s SCpcn

.
2
 mt  [
(
)
RTF   1
 1
 1 1 / 2
]
At p c
gives:
p c  {[

RTF
(
2
)
 1
 1
 1 1 / 2
]
1
At n 1
}
 s SC
, Pa
Internal Ballistic Analyses for Steady & Nonsteady Operation of SRMs
• Once chamber pressure established, can
in turn estimate thrust and specific impulse
delivered by SRM, via nozzle flow
calculations discussed earlier:
pe
F  C F At pc  C F ,v [ 1  (
)
pc
 1

] 1 / 2 At pc  ( pe  p ) Ae
 1
1

2  1 1 / 2
m t  m e 
At pc  [
(
) ] At pc
c*
RT F   1
I sp
F

m g o
• For more general steady or unsteady flow
analysis, use some form of the
conservation equations for gas and
particle flow; for 1D flow:
4 rb
4 rb
 ( u )
1 A


u  ( 1   p ) s
(
  )
t
x
A x
d
d
 p
t

(  p u p )
x
4 rb
4 rb
1 A

 pu p  p s
(
  ) p
A x
d
d
, gas
, particles
, conservation of mass (continuity)
p
4 rb
( u ) 
1 A 2
2
 ( u  p )  
u  (
  )u  a  
D
t
x
A x
d
mp
4rb
u 2 f

(1   p )  s u i 
d
2 d
(  p u p )
t

(  p u p 2 )
x

, gas
p
4r
1 A
 p u p 2  ( b   ) p u p   p a  
D
A x
d
mp
4rb

( p  s u i )
d
, particles
, conservation of linear momentum
D
d m2
8
C d  (u  u p ) u  u p
, drag interaction on
one particle
E = p/[(-1)] + u2/2
4r
( E ) 
1 A
 ( uE  up )  
( uE  up )  ( b   )E
t
x
A x
d
v 2f
p
4 rb
 ( 1   p ) s
( C pT f 
)  ua 
(upD Q)
d
2
mp
(  p E p )
t

(  p u p E p )
x

, gas
4r
1 A
(  p u p E p )  ( b   ) p E p
A x
d
v 2f
p
4 rb
 p s
( C mT f 
)   p u p a 
(upD Q )
d
2
mp
, particles
, conservation of energy
Ep = CmTp + up2/2
Q  d m k  Nu  (T  T p )
, heat transfer to
one particle
Quasi-Steady Flow
• Finite-difference format in preparation for
1D steady numerical solution:
_____
 2 u 2 A2  1u1 A1  rb S[(1   p )  s   ]  B1
_____
, gas
_
 p 2u p 2 A2   p1u p1 A1  rb S[ p  s   p ]  B1 p
, mass continuity
, particles
 2u 22 A2  p2 (
______
2
A1  A2
A  A2
u f
)  1u12 A1  p1 ( 1
)  S[(1   p )  s rb ui  rb u 
]
2
2
8
__
____
_____
__
A1  A2  p _ _
(
)[
D   a ]x  B2
2
mp
, gas
__
 p 2u 2p 2 A2

 p1u 2p1 A1
A1  A2  p _ __
  p  s rb ui S  rb uS  (
)[
D   p a ]x  B2 p
2
mp
_______
________
, particles
, conservation of x-momentum
 2u 2 A2 (C pT2 
u 22
2
)  1u1 A1 (C pT1 
u12
2
__ __
)  S[rb  s (1   p )(C pTF 
__
2
__
v w2
2
)
__
A1  A2  p ____ _
A1  A2 __
u
 hc (T  Tw )  rb  (Cv T  )]  (
)
(u p D  Q)x  (
) u a x  B3
2
2
mp
2
_
 p 2u p 2 A2 (C mT p 2 
u 2p 2
2
____
_
)   p1u p1 A1 (C mT p1 
__
u 2p
u 2p1
2
__ __
)  S[rb  p  s (C mTF 
__
v w2
2
)
__
p
____
_
A1  A2
A1  A2 _____
 rb  p (Cm T p  )]  (
)
(u p D  Q)x  (
)  p u p a x  B3 p
2
2
mp
2
_____
__
, gas
, conservation of energy
, particles
p2   2 RT2
, eqn. of state
Proceed to solve by substitution:
u2 

C p B2 
R
 {(
C p B2 
B1 C p B1
)  4( 
) B3 }1/ 2
R
2
R
B C p B1
2( 1 
)
2
R
2
 = 2A2/(A1+A2)
Once u2 is known:
 2  B1 /( A2u2 )
p2  2( B2  B1u2 ) /( A1  A2 )
T2  u2 ( B2  B1u2 ) /(RB1 )  p2 /(R 2 )
Now, for the particle phase:
 p2  B1 p /( A2u p2 )
u p 2  B2 p / B1 p
Tp2 
B3 p
B1 p C m

u 2p 2
2C m
• Proceed to calculate flow through finite
segments from i =1 (head end) to grain
exit, and for two-phase flow, continue from
there through to the nozzle throat, where
convergence is established when u/b = 1,
b being the non-equilibrium 2-phase sound
speed at that location; for single gas
phase cases, convergence when u/a = 1
at throat
Simpler Transient Problems
• Consider a simple uniform chamber filling
problem:
.
.
d
VC
 m in  m e
dt
Isothermal assumption, T = TF :
dpc RT F

2

[  s SCpcn  {
(
)
dt
VC
RT F   1
VC
t   dt 
RT F
p1

 1
 1 1 / 2
}
At pc ]
 1
2  1 1 / 2
n
1
[

SCp

{
(
)
}
A
p
]
dp c
t c
p s c RT F   1
0
Proceed with numerical solution up to equilibrium chamber pressure level
• Similarly, one can do a simple chamber
emptying problem (isothermal case):
 1
dpc
RT F .
RT F 
2  1 1 / 2

me  
{
(
) } At pc
dt
VC
VC RT F   1
 1
RT F

2  1
pc ( t )  po exp[ 
{
(
) } At  t ]
VC RT F   1
Here, one has an analytical solution to the problem.
20
10
sea level
Thrust, kN
Pressure, MPa
15
10
5
5
0
0
0.0
0.5
1.0
1.5
Time, s
2.0
2.5
0.0
0.5
1.0
1.5
2.0
2.5
Time, s
Predicted quasi-steady pressure-time and thrust-time profile
for a small cylindrical-grain motor. The initial ignition phase was not
modelled for these graphs (if desired, one could implement the
uniform chamber filling algorithm discussed earlier to approximate
the transient ignition phase).
Transient Burning in SRMs
• Transient behaviour in motors associated
with ignition (filling) and tailoff (emptying)
phases, and undesired pressure wave
activity during the main quasi-steady firing
phase
• A Zeldovich-Novozhilov approach that ties
in the energy of the solid phase beneath
the flame can be used to incorporate the
transient effect on burning rate
General equation for instantaneous unconstrained burning
rate:
0
1


rb  rb, qs 
Tdy
(Ts  Ti  H s / C s ) t


rb, qs ( p )  Cp n
 2T
T
k s 2   sCs
t
y
, quasi-steady value
due to local pressure
, movement of heat energy
within the solid phase
drb
 K b (rb  rb )
dt
1
Kb 
t
10
, damping eqn.
, for lagging rb*
Kb = 170000 s-1
Kb = 35000 s-1
Limit Magnitude
Kb = 1600 s-1
M 
5
0
0
5000
Frequency, Hz
10000
rb, peak  rb,o
rb,qs, peak  rb,o
Limit Magnitude
5
, varying Hs
s = +30000 J/kg
s = +100000 J/kg
s = +150000 J/kg
0
0
1000
2000
3000
Frequency, Hz
10
rb = 0.02 m/s
rb = 0.01 m/s
varying base burning rate
Limit Magnitude
rb = 0.005 m/s
5
0
0
5000
Frequency, Hz
10000
Axial & Transverse Combustion Instability of SRMs

may see chuffing or sputtering during ignition/filling phase, lowfrequency axial mode of instability
f1L  a/(2c)
Pressure, MPa
Pressure, MPa
• at higher frequencies, nonlinear axial combustion instability pertains
to the appearance of a sustained axial pressure wave moving back
and forth within the motor core flow, and in more severe cases, the
wave will have a steep shock compression front
• may be accompanied by a second symptom called a “dc shift”,
where there is a base chamber pressure rise
20
20
10
0.148
0.149
Time, s
10
0.10
0.15
Time, s
0.150
T-Burner for C.I. Testing
Schematic diagram of conventional T-burner for frequency-dependent
burning evaluation, showing different standing axial wave modes (first to
third harmonic).
• Traditionally, one attributes c.i. symptoms to be entirely a
function of combustion response (to transient pressure
or flow above the burning surface)
• More recently, influence of other mechanisms, like
normal acceleration via radial vibration, are being
considered as possible contributors to observed
symptoms, working in conjunction with transient
combustion response
• Vortex-shedding instability is a form of axial combustion
instability, generally producing low-level axial pressure
waves as a result of flow interaction with gaps that exist
in segmented propellant grain configurations (generally,
big SRMs which require segments of propellant, rather
than one monolithic propellant block)
• Transverse c.i. associated with tangential
and radial pressure wave activity in the
combustion chamber
f1T  0.59a/d
f1R  1.22a/d
• For suppression of transverse instability symptoms, the
use of 1 or 2% loading of particles of a suitable mean
diameter have proven to be effective
• Particles may be inert (like aluminum oxide) or reactive
(like aluminum, a fuel); generally, inert particles tend to
be more effective for suppression of c.i.
• Even at loading percentages of 20%, particles may not
be entirely effective for suppression of axial c.i.
symptoms
• Other techniques for instability suppression exist,
including modifying the propellant grain shape, or using
rods that act to defeat pressure wave development
Structural Issues for SRMs
• SRM motor casings typically composed of
metal (steel, aluminum, titanium alloys) or
composites (filament-wound for greater
strength)
• Pressure vessel approach to designing
casings (thin-wall theory, thick-wall theory,
finite-element modelling, etc.)
• Solid propellants are largely
incompressible, and don’t bear much
structural loading
Propellant
Casing
Head end
Nozzle
Sleeve
Port
Simple schematic diagram of a cylindrical-grain SRM with a steel static-test
sleeve surrounding a flightweight aluminum motor casing.
Port radius, m
0.03
0.02
0.01
0.00
0.0
0.5
1.0
Axial distance, m
Predicted port grain radius profile for reference cylindrical-grain SRM, with
(solid curves) and without pressure loading (dashed curves), at 0.25-sec
increments as grain burnback progresses upward towards the insulation/wall
boundary at the 3.2 cm radius position. Propellant deflection is relatively minor,
in this example.
Finite element mesh for star-grain SRM, 36 pie section, with
aluminum casing, and steel static-test sleeve. At left, start of firing (no
burnback), and at right, 28% grain burnback (later into firing).
• Exhaust nozzle experiences the most severe heating,
especially intense in the vicinity of the nozzle throat
• Common to see the use of graphite throat inserts to
prevent excessive erosion in that region; ablative
protective layers upstream and downstream of throat
• Nozzleless motor one way to get around the structural
issues associated with a traditional convergent-divergent
nozzle:
ROBOT-X
Canadair CL-289 recon drone; SRM boost
off launch rail, cruise thrust via KHD T117
turbojet engine (100-N thrust)
CL-289 being prepared for launch, German army
Circa 2004
Parachute/airbag landing/recovery of CL-289