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Integrated Design of a Hybrid Sounding Rocket using Liquid N2O
Jun-Young Heo*, Min-Gyoung Cho*, Hyung-Ju Park*, Soo-Jong Kim*,
Hee-Jang Moon**, Jin-Kon Kim** and Hong-Gye Sung**
*
Graduate School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang, Gyeonggi, South Korea
**
Department of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang, Gyeonggi, South Korea
([email protected])
Abstract: A hybrid sounding rocket using a commercial seamless aluminum tube has been designed. An integrated design technique
including engine performance, aerodynamic stability, and flight trajectory was developed. Liquid nitro oxide (LN2O) self-pressurized
in a tank is supplied into a 7 port fuel grain of polyethylene (PE). The specification of a hybrid sounding rocket carrying 1.2 kg
payload to 20 km altitude at launching angle of 85° is as the following: diameter 0.17 m, total length 4.40m and gross weight 98 kg.
The internal ballistic model including the oxidizer feed characteristics predicted hybrid rocket propulsion performance with confident
validation with experimental data. Both of trajectory simulation and aerodynamic analysis were evaluated by comparisons with
previous researches.
Keywords: Hybrid sounding rocket, Engine performance, Aerodynamic analysis, Trajectory optimization
1. INTRODUCTION
A hybrid rocket is one of various types of chemical
propulsion rockets. A common hybrid rocket uses solid fuel
and liquid oxidizer for its propellant. Main advantages of a
hybrid rocket are following: (1) safety during fabrication,
storage, or operation without any possibility of explosion or
detonation; (2) start-stop-restart capabilities; (3) relatively low
system cost; (4) higher specific impulse than solid rocket
motors and higher density-specific impulse than liquid
bipropellant engine; and (5) the ability to smoothly change
motor thrust over a wide range on demand [1]. Because of
these advantages, many universities and laboratories are
researching on hybrid sounding rockets [2-4]. Also, the
successful flight of the Space-Ship-One using polyethylene
and liquid nitrogen dioxide proved the possibility of the hybrid
rocket for space launcher [5].
This research is aimed at the development of a hybrid
sounding rocket, satisfying design requirements and
constraints. The integrated design including propulsion,
trajectory and aerodynamics was implemented for this study.
The oxidizer feed characteristic and local regression rate of
fuel grain are to be very accurately predicted because
combustion characteristic is intimately associated with the
mass flow rate of oxidizer and regression rate of fuel. To
determine the initial rocket configuration with payload,
oxidizer tank, rocket motor, and the other parts rocket motor
are assembled and examined by the solid modeler, CATIA.
The rocket configuration was finally determined after
investigating if the ballistic trajectory and stability of the
rocket satisfies the system requirements.
2. REQUIREMENTS AND DESIGN PROCESS
seamless aluminum tube is available to be used to a
combustion chamber and a liquid oxidizer tank for an
economic rocket. The fuel is made of polyethylene and the
oxidizer is liquid nitro oxidizer as listed in Table 1.
2.2 Design process
In this study, an integrated design process of hybrid rocket,
including propulsion system design, aerodynamic performance
calculation, and trajectory simulation was developed. This
approach enabled us to analyze and make necessary changes
of system characteristics based on predictions of the powered
and unpowered parts for rocket design [6-8]. Figure 1 shows a
typical design process of the hybrid rocket: a baseline rocket
configuration can be modified through detail iterative
calculations to satisfy the mission requirements.
Fig. 1 Design procedure for a sounding rocket
2.3 Configuration
2.1 Design requirements
Table 1 Design requirement
Fuel
PE
Oxidizer
Liquid N2O
Altitude
20 km
Payload
1.2 kg
Chamber Pressure
35 bar
Rocket Diameter
170 mm
Case Material
Commercial tube
The system requirement of a hybrid rocket is to carry 1.2kg
payload to 20km altitude with commercial pipe tubes for
rocket. Concerning the current market information, a 170 mm
Fig. 2 A typical configuration of a hybrid rocket
Figure 2 represents a typical configuration of the rocket
designed for this study. The rocket consists of an ogive cone
nose, a telemetry section, an oxidizer tank, a combustor, fins
and three launch lugs.
The fuel mass flow rate is function of the regression rate( r )
and grain configuration.
3. PROPULSION
where ρf, Ap and L represent the solid fuel density, grain
cross area and grain length. The regression rate is calculated
using an empirically-determined power law correlation
ascertained from the literature as
3.1 Internal ballistic model
The oxidizer mass flow rate and regression rate of fuel
grain are the major factors to accurately predict rocket
performance. The oxidizer mass flow rate highly depends on
the tank pressure and temperature because LN2O in tank or on
supply system may changes from liquid to gas below certain
pressure for motor operation. The motor performance
prediction code takes account several important factors
affecting on rocket performance: (1) N2O phase change which
may occur during supply from a tank to injector exit, (2)
transient process at ignition and tail off after combustion
process, (3) variable regression rate of fuel considering
air-fuel ratio changing during rocket operation, (4) variable
thermodynamic properties changing during rocket operation.
Figure 3 represents internal ballistic performance prediction
process of a hybrid rocket.
 pL
m f   f rA
(2)
r  aGoxn
(3)
where a, n are empirical parameters and Gox is the oxidizer
mass flux. The mass discharging out of the nozzle is
represented by the conventional choked flow equation.
 1
m out
 2   1
   1

 m *  Pc At 
 RTc
(4)
where At is the cross area of nozzle throat. R is the gas
constant. Tc is the chamber temperature. And  is the
specific heat ratio of combustion gas.
The mass flow rate for the oxidizer is computed the below
equation.
m ox  CD Ai 2 ox ( Pox  Pc )
(5)
Ai is cross section area of injector ports. ρox is the oxidizer
density. The discharge coefficient(CD) is obtained from
experiment. To simplify the combustion model, the chamber
temperature was assumed to only be a function of oxidizer to
fuel ratio and pressure, also combustion gas species are
assumed to have reached equilibrium composition. Thus,
thermodynamic properties can be obtained using CEA [10].
The time variant governing equations are solved by a 4 step
Runge- Kutta.
3.2 Model validation
The internal ballistic calculation code was validated by the
comparison with the 600kgf-thrust hybrid rocket motor test.
Test motor used PE as the solid fuel and liquid nitrous oxide
as the oxidizer.
Table 2. Specification of a test motor
Fig. 3 Performance prediction process of a hybrid motor
The oxidizer tank pressure(Pox) is assumed to
continuously change. Employing mass conservation of fuel,
oxidizer and combustion gas chamber pressure(Pc) can be
expressed as the following eq. (1) [9].
Initial port diameter
18 mm
Grain length
0.66 m
Grain of port
7
Nozzle throat diameter
38 mm
Initial ox. tank pressure
56 bar
Burning time
6 sec
Fig. 4 Schematic of hybrid rocket motor
dPc RTc
 b

 m ox  m f  m out   g rA
dt
V
(1)
Fig. 5 Photograph of a firing test
The specification of a test motor is presented in Table 2.
Figure 5 shows a photograph of a typical firing test of the
motor.
Fig. 6 Chamber pressure vs. operation time at pre-chamber of
test motor
Figure 6 shows the comparison of combustor pressure
based on theoretical formulation with the experiment. The
prediction data from ignition to tail off of combustion has
good agreement with the experiment with combustion
efficiency about 93%. The combustion efficiency ( ceff ) is
defined as the following formulation [11].
*
*
cactual
 C * ctheoretical
eff
(6)
The combustion efficiency 93% is acceptable value as
presented in previous research suggesting the value between
87% and 96% [1]. Figure 7 represents the predicted thrust and
the measured thrust of the hybrid motor test. The prediction
data tends to decrease similar as chamber pressure, but the test
data seems to be almost constant. The discrepancy can be due
to several reasons. The most suspect reason is that the data
error acquired from a road cell during the fire test because the
measured value at the end of the test was not null point
calibrated value before the test but offset about 50kgf. So the
measured data has the error bound at least 50kgf during firing
test. However, a detail analysis is necessary to figure out the
reason why the ignition transient and its peak value tend to be
slower and smaller than its prediction value. Multiport grain
configuration may delay and attenuate the pressurization
propagated form pre-chamber to post-chamber because the test
data is almost same as the predicted pressure history.
rocket must be stable so that it returns to the equilibrium
position when marginal disturbance occurs.
Fig. 8 Aerodynamic characteristics for static stability
Aerodynamic prediction was performed to calculate the
static aerodynamic coefficients and aerodynamic loads. To
verify accuracy of the prediction, the configuration considered
for validation is a conventional body-tail rocket [12]. In
comparison with the wind tunnel test, it has good results with
reference data as shown in Fig. 8.
The rocket is statically stable if the static margin of
unguided rocket is positive and the slope of the pitching
moment versus the angle of attack curve is negative. For
reasonable static margin of rocket, the fin was designed
through iterative processes changing the control surface size
and configuration.
The rocket is stable at 10-15 degrees of angle of attack as
shown in Figs. 9-10.
Fig. 9 Static margin vs. angle of attack
Fig. 7 Thrust vs. operation time of test motor
4. AERODYNAMICS AND TRAJECTORY
4.1 Aerodynamics
Aerodynamic design determines rocket configuration
satisfying the requirements of aerodynamic performance. A
Fig. 10 Pitching moment coefficient vs. angle of attack
4.2 Trajectory
The ballistic trajectory analysis using 2DOF and 3DOF
equations was performed. Figure 11 shows the flight altitude
and flight Mach number. The maximum altitude is
approximately 20 km at 63 seconds. Flight Mach number
reaches at the maximum value 2.25 at burnout time, 10
seconds and decreases after burn out, but increase again after
the rocket reaches at maximum altitude due to energy change
from potential energy to kinetic energy.
Fig. 11 Flight altitude and flight Mach number vs. flight time
5. SPECIFICATION OF THE HYBRID ROCKET
Through the integrated design process described in
previous sections, the finally designed hybrid rocket is
powered by a 7100N thrust motor to reach at altitudes 20km.
Specifications of the rocket are listed in Table 3. The rocket
has no recovery system like a parachute because the rocket
with recovery system has too large ratio of length to diameter
(L/D) of the rocket to be stable if the diameter does not
increase.
Table 3. Specification of the hybrid rocket
Fuel
PE(7ports)
Oxidizer
Liquid N2O
Altitude Performance
20 km
Payload
1.2 kg
Burn Time
10 sec
Chamber Pressure
35 bar
Total Impulse
71,000 N-sec
O/F
6
Fuel Total Mass
12.6 kg
Oxidizer Total Mass
28.6 kg
Total Weight
98.3 Kg
Motor and Fuel Tank Case Material
Commercial Seamless
Aluminum Tube
6. CONCLUSIONS
An integrated design technique including engine
performance, aerodynamic analysis, and trajectory
optimization was developed, validated, and finally applied to
design a hybrid rocket. The rocket configuration was finally
determined after an iterative design process if the ballistic
trajectory and rocket stability satisfies the system requirements.
The specification of the rocket is described in Table 3. The
rocket’s weight, moment of inertia, and component assembly
check were confirmed by the solid modeler, CATIA.
ACKNOWLEDGMENTS
This research was supported by Basic Science Research
Program through the National Research Foundation of
Korea(NRF) funded by the Ministry of Education, Science and
Technology. (No. R0A-2007-000-10034-0)
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