44th International Conference on Environmental Systems
13-17 July 2014, Tucson, Arizona
ICES-2014-104
Characterization of Combustion in a Hybrid Rocket Motor
Paraffin-Based
Saulo A. Gómez1, Shirley Pedreira2 and Pedro Lacava3
Instituto Tecnologico de Aeronáutica, São José dos Campos, Brasil, 12228-901
A hybrid rocket motor is an intermediate choice between solid and liquid propulsion
systems. The use of paraffin as fuel increases the regression rate because of the formation of
droplets originated from a process of hydrodynamic instability on the oxidant-fuel interface.
Chamber pressure is measured in a laboratory test with a hybrid configuration that uses
paraffin and gaseous oxygen. In addition, a numerical solution of the continuity equation is
applied to the combustion chamber, using an algorithm that takes into account physical and
thermo chemical properties of the propellants as well as the internal geometry of the motor.
Finally, numerical and experimental results are compared.
Nomenclature
Ac
Ai
Cd
L
P0
R
Rg
T0
V
a
ṁox
n
r
t
δ0
δp
δox
γ
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
critical area of the nozzle
injection area
discharge coefficient
length of the fuel grain
chamber pressure
instantaneous radius of the fuel grain
constant for ideal gas model
flame temperature
instantaneous volume of chamber
constant of the burning rate
mass flow of the oxidant
exponent of the burning rate
burning rate
time
density of gas on the chamber
grain density
density of the oxidant
specific heat ratio
I. Introduction
I
N a hybrid propellant rocket, fuel and oxidant are stored separately in different phases, this concept of propulsion
is shown in figure 1. According to Sutton & Biblarz, the most common hybrid configuration is solid fuel and the
oxidant can be in liquid or gas form. Hybrid propulsion is restartable, due to oxidant supply can be regulated. In
addition, it offers safe manufacture and operation.
Hybrid propulsion is considered as an alternative way of chemical energy conversion stored in propellants into
kinetic energy1. This energy is applied in propulsive systems of manned platforms, maneuvering procedures and
repositioning of micro satellites. It is a system of minimum environmental impact and lower cost than traditional
systems based on liquid or solid propellants.
1
Master student, Propulsion Department, sagomezs@unal.edu.co.
PhD Student, Propulsion Department, shirley@ita.br.
3
Professor, Propulsion Department, placava@ita.br.
2
Oxidant propellant
Combustion chamber
Fuel propellant
Figure 1. Hybrid rocket concept, adapted from Sutton.
A composition paraffin-black carbon is used as fuel on the experimental rocket motor, whereas the selected
oxidizer is gaseous oxygen. Particles of black carbon improve mechanical characteristics of the grain 4. Paraffin,
C20H42, is an alkane whose molecular mass is 282,6 g/mol. The stoichiometric reaction can be written as:
C20H42 + 30,5O2 →20CO2 +21H2O
The percentage of black carbon is 4%. The grain is made according the process described by Santos, Mota e
Lacava, 2012. In order to form the inner hole, øi = 10mm, centrifugal action is used while solidification is occurred.
Final dimensions of the cylindrical bar are: ø 32.8mm x 150.0mm
Paraffin presents a regression rate that can reach three or four times other fuels for hybrid configurations,6 since
the liquid layer formed on the burning surface ensures high regression rate when convected into the flame front.
II. Numerical Approach
The mass balance equation in a hybrid rocket motor is presented by Sutton as:
(
)
̇
̇
(1)
a and n are empirical constants that depend on the propellant composition. Whereas ṁox is determined by the
pressure difference between the supply tank and the chamber, the complete expression is:
√ (
̇
)
(2)
c is a constant, function of the properties of the combustion products:
√
(
)
(3)
If the pressure function, P0, is continuous and differentiable at the time interval A-B, Figure 2, an algorithm
based on finite differences to solve P0 can be implemented. The interval is divided in a finite number of sub-intervals
with width Δtj each one.
Figure 2. Numerical approach for the pressure chamber.
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International Conference on Environmental Systems
In order to value numerically Eq (1), it is discretized on the same way described in Gómez, 2013. An implicit
equation for P0 is resolved to obtain the transient comportment of the pressure chamber, due to V and R are function
of P0 and all other parameters of Eq (1) are known, which are indicated on the table 1
Table 1. Numerical Inputs
T0
3110 K
Rg
208.19
γ
1.21
n
0.62
a
1.17 x 10-4 m2n+1sn-1/kgn
δp
840 kg/m3
L
0.15 m
Cd
0.7
Ai
5.5x10-6 m2
Pi
3 MPa
Ac
31 x 10-6 m2
The plot of P0 evaluated with this discretization is presented in the figure 3.
III. Experimental Results
A test with the hybrid motor was conducted using 3 MPa as pressure of injection, a sketch of the experimental
setup is shown on the figure 3.
Figure 3. Experimental setting of the hybrid motor5
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Numerical and experimental plots are presented on the figure 4.
20
Pressure Chamber, bar
18
16
14
12
10
8
Experimental
6
Numerical
4
2
0
0
1
2
3
4
5
6
7
Time, s
Figure 4. Numerical and experimental results
Both plots show a low variation during the combustion, with a difference of approx. 15% on the mean pressure.
Nevertheless, the total time differs considerably, more than 50%. One reason of this high change is the short
diameter of the chamber that limits the burning time. Consequently, uncertainties are more significant. The
simulation can be improved if properties of the exhaust gas are measured directly, instead of use assumed values.
IV. Conclusion
The numerical approach based on finite differences is appropriate to predict the chamber pressure during the
combustion process. These results can be used to anticipate the performance and the given power of a hybrid rocket
motor.
Although experimental results show acceptable agreement with the proposed model, more laboratory tests under
different conditions should be conducted in order to verify the numerical implementation and the range where it is
valid.
The model would be improved if other phenomena like chemical reactions more complex, thermal and kinetic
losses are included.
In order to reach a longer time of combustion, diameter of grain can be increased, due to the chamber pressure
not change considerably during the burning. In a solid propellant (fuel and oxidant are contained on the same grain)
under radial burning, other effect is observed, the pressure is higher on the end of the combustion 3. Therefore, a
superior stress is supported by the chamber wall and it grows with the time burning.
References
Books
1
Sutton, G.P. and Biblarz O., Rocket Propulsion Elements, 8th ed., John Wiley and Sons, New York, 2010.
2
Humble, R.W; Henry, G.N; Larson, W.J. Space Propulsion Analysis and Design, 2nd ed., McGraw-Hill, 1995. Space
Technology Series, United Spaces Department of Defense and the Aeronautics and Space Administration. 748p..
Proceedings
3
Gomez, S., Ceron, H., Murcia. Dynamic Model of the Internal Pressure in a Solid Propellant Rocket Motor. 22nd
International Congress of Mechanical Engineering – COBEM2013. Ribeirao Preto, Brasil.
4
Lacava, P.T; Barros, T. M. Protótipo de Motor Foguete Movido a Propelente Híbrido. 2010. XVI Meeting of Scientific
Initiation and Graduate ITA - XVI ENCITA / 2010 Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil,
October 20, 2010.
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Santos, G.P; Pedreira, S.M; Lacava, P.T. Phisycal Property and Carbon Black Distribution Impact on Propulsion Efficiency
of Paraffin-Based Fuel. 2012. ASME, Proceedings of the International Mechanical Engineering Congress & Exposition,
IMECE2012, November 9-15, 2012, Houston, Texas, USA, pp 1-13.
Reports, Theses, and Individual Papers
6
Karabeyoglu, M. A. Scale-up Tests of High Regression Rate Liquefying Hybrid Rocket Fuels. AIAA 2003-6475. Stanford
University Stanford, CA and NASA Ames Research Center Moffet Field, Mountain View, CA. June, 2003. Pp 1-19.
7
SALVADOR, C. A. V. Investigação Experimental de um Propulsor Híbrido para Satélites e Veículos Espaciais Usando
Parafina e N2O4 como Propelentes. 2009. Tese de Doutorado do Curso de Pós-graduação em Engenharia e Tecnologia
Espaciais/Combustão e Propulsão. Instituto Nacional de Pesquisas Espaciais, S. José dos Campos, S. Paulo, 179p.
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