International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 2- September 2015
An Overview of Composite Propellant Burning
A. M., Hegab#1, S. A. Gutub*2
#1
Mechanical Engineering Department, Faculty of Engineering at Rabigh,King Abdulaziz University, Saudi
Arabia
*2
Civil Engineering Department, Faculty of Engineering at, King Abdulaziz University, Saudi Arabia
Abstract An overview of theoretical and
experimental work concerning the burning process in
rocket propellant is presented. A mathematical model
for the 2D random packing discs strategy of rocket
propellants and their burning is implemented. The
current study has emphasized Ammonium Perchlorate
(AP) / Hydroxyl Terminated Poly-Butadiance, (HTPB)
composites rocket propellant. These propellants are
widely used in a variety of rocket systems ranging
from small tactical missiles to the large boosters that
propel the space shuttle into orbit. A detailed review
for the chemical kinetics, numerical and experimental
models for the burning of the monomodal, bimodal,
and multimodal propellants is introduced. Effects of
propellant compositions, time-dependent pressure
fluctuations, temperature, fuel-binder types, on the
burning rate are reviewed and discussed. The result
of the current study shows the effect of pressure and
the AP particle sizes on the burning rate, the complex
flame structure, and the morphology of the
combustion surface.
Keywords Composite propellant, solid particles,
spheres and discs packing, sandwich propellant,
AP/HTPB.
I. INTRODUCTION
The designers of solid propellant rockets are still
facing several technological problems. These
problems require expertise in several diverse research
areas. On the other hand side, in order to have a stable
engine with high performance, the detailed wholesystem simulation of the solid rocket motors must be
achieved first. The entire integration must include the
modeling of; "(1) the ignition and combustion of
composite energetic materials, (2) the solid mechanics
of the propellant, (3) the case and insulation, (4) the
nozzle and the fluid dynamics of the interior flow and
exhaust plume, (5) the shock physics and quantum
chemistry of energetic materials"[1,2]. As a result,
most of the research studies within the last three or
four decades have been conducted to examine some of
these models separately in order to acquire some
information about the complex flame structure and the
nature of the generated flow field inside the solid
rocket motor chamber.
The coupling and feedback between the pressure
oscillations and the burning rate can lead to instability,
called ―combustion instability‖. In another word,
pressurization of the crack causes it to grow rapidly
and may be the burning reach to the rocket casing in
very short times through the crack causing a
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catastrophic failure for this reason, relatively small
defects can lead to catastrophic failure such as the
famous Challenger accident many year ago. For
further information about the combustion instability,
see Ref. [3,4,and 5]. Generally, the origin of the
instability in the operation of Solid Rocket
Motor(SRM) is probably associated with combustion
process of the heterogeneous propellant. The burning
of the solid propellant of energetic materials, it is our
believe, is the back-pone for the whole system
simulation, since it is the deriving thermo-mechanical
force in the operation of a solid rocket motor.
As a result, the objective of the current review is
concentrated on a model of the solid rocket motor
propellant combustion which play an important roles
in the dependence of the burning rate on pressure.
Rocket propellants may be divided into two general
classes, double-base propellants and composite
propellants. The principle components of the double
base propellants are nitrocellulose and an explosive
plasticizer, usually nitroglycerin, [6-9], while the
composite propellants are made by embedding a finely
divided solid oxidizing agent in a binder. Regarding
the latter composite propellant, oxidizing agents which
have been used extensively include, ammonium
perchlorate. The materials which have been employed
as binders are, asphalt, natural and synthetic rubbers,
vinyl polymers, polyesters, and nitrocellulose.
Ammonium picrate, carbon black, and aluminum
powder have been used as fuel fillers [10].
The current review and study has emphasized the
composite propellants because they have been of
greatest general interest over the modeling time period.
The modern rocket composite propellant mixture
consists of the following ingredients [11];
an
Ammonium Perchlorate (AP) as oxidizer, aluminium,
iron oxide, Hydroxyl Terminated Poly-Butadiance,
(HTPB) fuel binder, and an epoxy curing agent. AP,
NH4ClO4, based composite propellants are widely
used in a variety of rocket motor systems ranging from
small tactical missiles to the large boosters that propel
the space shuttle into orbit. The properties used for AP
come from Tanaka and Beckstead [12,13] and Guirao
and Williams [14] . Solid AP passes through two
phases before melting.
Most of the thermodynamic and transport properties
used for HTPB come from the work of Parr and
Hanson-Parr [ adapted from 12], Jeppson et.al. [13],
W. Cai and V. Yang [15].
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 2- September 2015
II. SOLID AND GAS PHASES REACTIONS
The basic idea for the burning of the rocket
propellant is further illustrated in 1998 by Jeppson
et.al. [16,17,18], as shown in Fig.1. The composite
solid propellant is at a given initial temperature. As
the temperature increases, the AP portion of the
propellant undergoes a partial decomposition. With
further heating, the propellant ingredients can melt or
liquefy and the condensed liquid layer forms. This
condensed layer consists of many phases: solid to
liquid AP, liquid HTPB, and gas phase bubbles. These
bubbles contain the gaseous species formed by the
semi-global
condensed
phase
decomposition
mechanism for liquid AP and HTPB. The temperature
rises sharply as the gas phase flame develops in the
third region ―jump conditions‖.
During the last four decades, all the theoretical
studies for modeling of solid propellants assumed that
the regression of the surface function is constant with
time. Moreover, most of these work assumed that the
combustion surface is flat. In general these models
have been somewhat successful for given good insight
about the complex flame structure, but are not
sufficiently accurate, or complete to predict the effect
of the unsteady non-planar moving combustion
surface on the burning rate and, in turn on the complex
flame structure. Only the work by Jackson, et.al. [16]
considered the combustion surface has a non-flat
function (i.e. Hills or Valleys) and no serious attempt
has been taken to advance the regression of the surface
function to be dependent with time till the year 2001,
Recently, for the first time, Hegab, et.al. in 2001
[17,18] developed a mathematical model for the
complete coupling of the burning solid propellant.
Propagation of the unsteady non-planar regressing
surface is derived and written in details in Ref. [19-22].
R1 and R2 are assumed to have the forms
 -E 
R1 =B 1 P X exp  1 
 R uT 
 -E 
R 2 =B 2 P 2 ZY exp  2 
 R uT 
(2)
Where B’s are the exponential prefatory,
B. Gas Phase Equations
The corresponding gas phase equations are;
g
D   g 
  .(   )  R
Dt
cp
(3)
Qg1 R1 / c p  Qg 2 R2 / c p 


 R1



  R2



  R1   R2

T 
X 
 
Y 
 
Z  ,
(4)
The above equations represent the constant density
model, where;
 g Dg  g / c p
(5)
P=RT
C.
(6)
Solid-Phase and Solid/Gas Interface Equations
The energy equation is solved simultaneously with the
gas phase equation;
 s Tt 
s
cp
 2T
(7)
by setting;
  AP

s   AP
B
s  
 B
Fig. 2. The three phases of solid propellant
combustion [ 16 ].
 0
 0
,
(8)
where the subscript AP denotes to Ammonium
Percolorate and the subscript B denotes to the binder.
Suppose that;
(x(t),y(t),t)=0
or in the vector form
A. Two-Step Kinetic Equations
Recently, Hegab, et.al. (2014), [23] developed
"two-step kinetics that include the AP decomposition
flame and the final diffusion flame is examined first.
Thus;
R1
AP( X ) 
 decomposition products(Z )
R
 Z  Binder (Y ) 
 final products
2
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 

 t  V .    0, V  dx / dt, dy / dt  .

If n is defined to be;

(1)
n   /  ,
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 2- September 2015
The interface equation becomes;

t  rb  
 0,
disks with different sizes. We start with a periodic
arrays of 2D discs, and in one of these discs, an N
points are randomly placed, each of which is randomly
assigned a velocity. These points are kernels for the
AP particles that will eventually pack the disc. As
time advanced each kernel will grow with a certain
growth rate and move randomly through the packing
process.
(9)
where;
rAP  AAP ( P / P0 ) n AP exp  E AP / RuTAP,s 
rb  
n
rB  AB ( P / P0 ) B exp  E B / RuTB ,s 
 0
 0
(10)
 = y - f(x,t)
(11)
Vn
v
n
u
 = y - f(x,t)
Vt
rb
Fig. 4 Moving and growing of two spheres 1 and 2
from zero time to the first collision time (tc)
Figure 3 : Sketch showing the coordinate system.

n
 f x ,1
1  f x2
 
Vn  n . v 

, t 
 uf x  v
1  f x2
1, f x 
If two particles collide as shown in figure 20 before
the final packing is achieved, an additional centerline
force is given to make them move and continue
growing until the final packing density is satisfied.
More details about the packing algorithm and the
collision process will publish in somewhere else.
Figures 5-7 showed the 2D disk pack with packing
fraction 0.68 of AP for monomodal, bimodal and
Multimodal disk pack, respectively. The length scale
is 500 microns.
1  f x2
 
, Vt  t . v 
u  vf x
1  f x2
For no-slip boundary condition, Vt=0 which lead to;
u+fx v=0
(12)
and;
f t  rb 1  f x2  0,
(13)
D. Boundary/Jump Conditions
The conditions at the boundaries are derived in[23]
and written as;
m   v.n  rb   0
;

n.T   Qs m

mYi   Dn.Yi , i  1,2,3,
Q AP
Qs  
Qb
T   0
 0
 0
;
Fig. 5 Two-dimension disk pack with packing fraction
0.68 and monomodal disk pack
;
(14)
(15)
For all reactions."
III. RESULTS AND DISCUSSIONS
In this study, the packing strategy described the disk
pack model by assuming that the particles of the AP
are 2D disks and distributing them in a random
fashion and applied to a binary packs, distributions of
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Fig. 6 Two-dimension disk pack with packing fraction
0.68 and Bimodal disk back.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 2- September 2015
Fig. 7 Two-dimension disk pack with packing fraction
0.68 and multimodal disk back.
Fig. 8 showed the position of the surface at various
times, equally spaced, during the consumption of a
single square (randomly packed) of a periodic pack.
They added also some insight into the nature of the
combustion field supported by such a propellant as in
Fig. 6.
horizontal flame structures over the combustion
surface and lies adjacent to the small and large AP
grains. As time advanced, these horizontal shapes
converted to curved ones to reflect the burned portions
of the AP grains. The second flames are the diffusion
flames that generated at the interface between the AP
grains and the fuel-binder HTPB. These flames
represent the vertical flame structure at the interfaces
points between the fuel and oxidizer. As time
advanced, these diffusion flames take a different
shapes in the gas phase and may meet each other in a
very nice way to form another flames away from the
combustion surface.
Note that the base of some
diffusion flames found to be away from the interface
between the AP/HTPB region over the large AP grains.
This important phenomenon has been noticed by
others. The reason behind this shift to the location of
the diffusion flames may be related to the
stoichiometery and the flux conditions.
(a) t=t1
Fig. 8 The position of the surface at various times for
the bimodal disc back
The reaction rate contours generated from the
combustion of the 2D disc packs Fig. 6 is illustrated in
Fig.9 a and b. The combustion field is generating by
solving the full 2-D, gas equation in the gas phase
simultaneously with the energy equation in the solid
phase and the Hamilton-Jacobi equation for the
moving interface as described before with the
sandwich model [23]. This figure showed huge AP
decomposition zone much of the surface, but there
were other structures extending well from the surface
on a scale defined by the particle.
The upper part is the gas phase and the lower one
represent the solid phase. The circles region in the
latter represent the AP grains (gray), while the powder
around the circles represent the fuel-binder HTPB.
The combustion surface and the morphology of the
combustion surface is clearly shown. Moreover the
differences in shapes of the reaction rates contours R
with time illustrate the behaviour of the burning rate at
the propellant surface. In additions these figures show
two kind of flames. The first ones are the AP
decomposition flames. These flames represents the
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(b) t=t2
Fig. 9a, b: The reaction rate contours at two different
times
As the time advanced, a portion of the combustion
surface be very sharp at the end of the burning of the
large AP grains. Really these notches show the ability
of the current numerical modeling and the level set
strategy to deal with this sensitive changes. Moreover,
if anyone look carefully to the combustion surface will
find a portion of the surface has no flame, or in
another word the flame structure over the surface is
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International Journal of Engineering Trends and Technology (IJETT) – Volume 27 Number 2- September 2015
not continuous. This can occur if the packing process
form a fuel-rich regions. Really, this phenomenon is
not desired in the rocket propellant burning since it
may lead to extinction and in turn rocket failure.
very cloe to the real one. In addition the AP size and
the size distribution has a great effect on the burning
rate. The modeling packed propellants defined in this
way are used as the platform for the computational
techniques of burning propellants and a model which
accounts many complex different parameters. In
addition, the unsteady combustion of microscale
rocket propellant gave good insight about the transient
behaviuor of the burning process, but didn’t reflect the
acoustic instability on the large scale. Results of this
kind may used to develop the cold model as in 2015
by Hegab and Gutub with more realistic boundary
conitions.
ACKNOWLEDGMENT
A fruitful discussion with Prof. J. Buckmaster and
T. Jackson, UIUC, USA is deeply appreciated.
Fig. 10 The instantaneous mass of the ammonium
perchlorate.
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Fig. 11 The instantaneous burning rate.
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IV. CONCLUSIONS
[14]
The current study for the 2D disk random packing
models for the rocket propellant, demonstrated that
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packed theoretically with particle-size distributions
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WITH
TRANSIENT
SIDEWALL
MASS
ADDITIONS‖ ,International Journal of Engineering Trends
and Technology (IJETT) – Volume (27) Number 1September. 2015
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