AIAA 2009-4966
45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
2 - 5 August 2009, Denver, Colorado
Mixtures of Nitrous Oxide and Oxygen (Nytrox) as Oxidizers for Rocket
Propulsion Applications
Arif Karabeyoglu*
Space Propulsion Group Inc.
Sunnyvale, CA
Abstract
Most of the oxidizers available to be used in chemical propulsion applications are
highly hazardous materials that are either toxic or explosive in nature. Among the
short list of oxidizing agents, liquid oxygen (O2) and nitrous oxide (N2O) stand out
as the most practical propellants due to their wide availability, broad base of use,
cost effectiveness and relatively benign nature. A new class of oxidizers (Nytrox)
which are composed of equilibrium or non-equilibrium mixtures of nitrous oxide
and oxygen are formulated in order to maximize the benefits of the pure
components while retaining their practical advantages. Note that in the mixture O2
serves as the pressurizing agent, whereas N2O is the densifiying component. The
primary advantages of this new system over the pure oxidizers can be listed as 1)
self pressurization capability, 2) high density and density impulse, 3) non-cryogenic
operational temperatures, 4) higher Isp performance compared to N2O, 4) improved
safety 5) efficient gas phase combustion and 6) easier development of stable and
efficient motors compared to liquid oxygen due to the exothermic decomposition of
the N2O molecule. Unlike the pure oxidizers, the mixture allows for two independent
control variables (temperature and pressure) which can be fine tuned to optimize
the system for a particular application.
I) Nomenclature
A:
a:
B:
b:
f:
k ij :
Coefficient for cubic equation of state
Attraction parameter
Coefficient for cubic equation of state
van der Waals covolume
Fugacity
Interaction coefficient for ith and jth components
m:
P:
Pc :
R:
T:
Tc :
Peng Robinson coefficient
Pressure
Critical pressure
Gas constant
Temperature
Critical temperature
Tr :
x:
Z:
Zc :
Reduced temperature
Mole fraction
Compressibility
Critical compressibility
α:
Function of Tr and acentric factor
*
President & CTO, Space Propulsion Group Inc., Consulting Professor in the Department of Aeronautics
and Astronautics Stanford University. Member AIAA.
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Copyright © 2009 by Arif Karabeyoglu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
v:
Specific volume
Acentric factor
ω:
II) Introduction
Unlike the wide range of fuels that are currently available to be used in chemical propulsion systems, the
list of potential oxidizers is quite limited. Figure 1 classifies the materials that can be used as oxidizing
agents in propulsion applications based on the chemical group that they belong to. Note that pure
chemicals and mixtures are listed separately. The general classes considered are halogens, oxygen based
materials, hydrogen oxides, solid oxidizers, oxidizes of nitrogen, nitric acid and other oxidizers which
include the mixed compounds of the elements oxygen, nitrogen, chlorine, fluorine and hydrogen. In order
to accesses the practicality of each oxidizer, red fonts are used for the highly hazardous (toxic or explosive)
oxidizers, whereas blue fonts are used for materials with poor performance. It can be shown that each
oxidizer on this short list can be associated with some significant shortcoming which adversely influences
its use as a practical propellant. For example, the high density storable oxidizer H2O2 has major safety
issues due to its tendency to self-decompose (and potentially detonate). The commonly used N2O4 is highly
toxic. Solid phase oxidizers used in solid rocket applications generally suffer from low Isp performance,
and widely used perchlorate based solid oxidizers raise significant environmental concerns.
Figure 1: Classification of oxidizers.
Based on these arguments, it is clear that development of new improved oxidizing agents would constitute
a critical technological enhancement in the field of chemical propulsion. The search for better oxidizers
requires a clear description of the desirable attributes for the oxidizing component of the propellant system
which can be listed as:
•
•
•
•
•
•
•
•
•
•
•
•
High Isp performance with common fuels
High density
Good combustion stability and efficiency characteristics
Chemical stability – for safety and long term storage
Low toxicity
Storability under normal conditions
Adequate self pressurizing for pressure fed systems (or low vapor pressure for pump fed systems)
Low freezing point
Hypergolic behavior with common fuels
Ease of handling
Low cost
Compatibility with tank and feed system materials
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III) Properties of O2 and N2O as Oxidizers
Note that two oxidizers, liquid oxygen (LOX) and nitrous oxide (N2O), that are listed in Figure 1 can be
isolated from the rest of the group as being the most practical materials due to their relatively low hazard
level, environmental friendliness, wide availability, broad base of use in other applications, low costs and
better than modest performance. These virtues resulted in the wide use of these oxidizers over a range of
propulsion applications.
Liquid oxygen is a high performance oxidizer which is commonly used in liquid and hybrid rockets with
substantial total impulse requirements due to its advantages that can be listed as
•
•
•
•
•
High Isp performance.
High chemical stability of the diatomic oxygen.
Wide experience base.
Low cost.
Low optimum oxidizer to fuel ratio reducing the fraction of liquids in the case of a hybrid system.
Despite its wide use LOX has some serious disadvantages.
•
•
•
•
•
LOX is a deep cryogenic material with a boiling temperature of approximately 90 K. This
introduces significant operational difficulties and inconveniencies. The low operational
temperature has an adverse effect on the mass fraction of the propulsion system due to 1)
requirement for a tank insulation layer to minimize the boil off and 2) limit on the range of
materials that can be used as the tank material (for example LOX capable composite tank
technology is still not available).
Motor stability and efficiency is hard to obtain. In the case of hybrid systems, stable and efficient
operation is typically achieved by adding a heating source at or around the injection point of the
LOX. This undesirable fix complicates the design and increases the cost and weight of the overall
propulsion system. For liquid rocket systems, it is well known that LOX engines running with
hydrocarbons such as RP1 tend to produce rough combustion. These systems typically require a
significant amount of development effort until the desired stability margin is attained.
LOX is almost never used as a self pressurizing oxidizer since the density is quite low at higher
pressures. For example at 50 atm the density of liquid oxygen is only 550 kg/m3.
LOX presents a strong dependency between density and pressure along its saturation line.
Oxygen cleaning of the feed system components is critical. LOX fires are common.
N2O has generally been the choice for relatively small rocket systems due to its self pressurizing capability
arising from its high vapor pressure at room temperature. Self-pressurization can be useful because it
eliminates the additional weight, complexity and cost of the pressurization system or the turbopump system
needed to feed a liquid oxidizer into the combustion chamber at high pressures. The other advantages of
N2O can be listed as
•
•
•
•
Stable and efficient combustion is easier to attain due to the exothermic decomposition reaction of
the oxidizer molecule.
Extensive experience base exists in the hybrid propulsion field.
Easily accessible chemical commonly used in several other industries.
Modest cost.
The following disadvantages limits the use of N2O to small systems
•
•
•
Low Isp performance.
Low density (when self pressurization is needed). At low temperatures the density can be
improved but the pressure drops significantly.
Low density impulse.
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•
•
•
High dependence of density and pressure on the temperature. Temperature conditioning is
required for most practical applications.
Nitrous oxide molecule has a positive heat of formation. Self decomposition in the tank, feed lines
and the combustion chamber is possible and might result in catastrophic failure.
System optimizes at high oxidizer to fuel ratios requiring a high mass fraction of liquids.
IV) Opportunity: Mixtures of N2O and O2
As shown in Figure 1, equilibrium mixtures of pure compounds have been widely used as oxidizers in
chemical propulsion. As long as the materials are miscible, mixtures within the same family (intrafamily)
and mixtures of substances from different families (interfamily) are both feasible. The interfamily oxidizers
are particularly interesting and are typically formulated for a specific reason. For example the primary
function of oxygen in the FLOX system is to limit the mole fraction of the heavy combustion product CF4
to maximize the Isp performance with hydrocarbon fuels.
A new possibility of an interfamily oxidizer, which has never been considered in the context of propulsion
applications, is the mixture of oxygen and nitrous oxide (Nytrox)1. Since these two materials that have
already been identified as the most appealing oxidizers from a practical sense, their mixture is also
expected to retain the practicality advantage. It is interesting to note that the mixtures of O2 and N2O have
been studied extensively, since the mixture is commonly used as anesthetic in medical/dental applications.
As discussed in Refs. 2 and 3, the two substances are highly miscible in the liquid phase which opens up
the possibility of using the mixture as an oxidizer for chemical propulsion systems which would potentially
maximize the benefits and eliminate the shortcomings of the individual components.
Specifically, the goal is to formulate a high density, self pressurizing oxidizer that does not have to operate
at deep cryogenic temperatures. Note that in the mixture, the oxygen is the volatile component which
serves as the pressurizing agent whereas the N2O is the less volatile one with the primary function of
densifying the mixture. A simplistic explanation of the Nytrox concept is given in Figure 2 which shows
the oxygen, nitrous oxide and the mixture of the two as a function of temperature in the oxidizer tank. At
deep cryogenic temperatures, oxidizer is liquid oxygen in its pure form. As the temperature is increased
mixtures of the two substances become feasible and the Nytrox oxidizers are formulated. As the
temperature increases, oxygen content of Nytrox decreases and finally at temperatures close to the room
temperature pure nitrous oxide becomes the practical oxidizer.
Figure 2: Nytrox concept.
The advantages of Nytrox oxidizers compared to its pure components can be summarized as
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•
•
•
•
•
•
•
Partial self pressurization possible at high densities (eliminates or minimizes the use of expensive
helium as pressurant).
Improved Isp performance compared to N2O.
Not a deep cryogen as liquid oxygen. Oxidizer at -80 C (or at warmer temperatures) is much easier
to manage. Composite tanks can be used.
Lower freezing point compared to pure N2O is expected. This is a useful virtue for space
applications.
Optimization based on mission requirements is possible. The critical control variables are the
temperature and pressure which determine the oxidizer mass fraction in the liquid and vapor
phases of the mixture.
Thermodynamic non-equilibrium mixtures can be used in order to increase the system
performance significantly.
The Nytrox systems are much safer than blow down nitrous oxide systems since the vapor phase
of the Nytrox system has a large O2 concentration, in the rage of 50-90 % by mass. A typical
Nytrox system with 70% oxygen in the vapor phase requires 4-5 orders of magnitude larger
ignition energy compared to pure nitrous oxide. In summary, Nytrox vapor is virtually impossible
to ignite with any conceivable ignition source.
A comparison of the LOX, N2O and Nytrox as oxidizers is summarized in Table 1. The table shows the
clear advantage of Nytrox over the pure substances in many key areas which would allow the designer to
formulate an oxidizer ideal for the particular application of interest.
Table 1: Comparison of pure O2, N2O and Nytrox as oxidizers.
Feature
O2
N 2O
Isp Performance
Density
Impulse Density
Chemical stability
Toxicity
Storability
Self Pressurization Capability
Gas Phase Combustion
Hypergolicity
Ease of handling
Material Cost
Chemical compatibility
Performance tuning capability
Motor Stability/Efficiency
Overall Safety
5: Best performance, 1: Worst performance
* He pressurization
5
4
4
5
5
1
1
1*
1
3
5
5
1
2
3
Nytrox
3
2
1
4
4
5
5
3
1
5
4
5
2
5
2
4
4
3
4
4
3
3
5
1
4
4
5
5
4
5
V) Properties of the O2/N2O Mixtures
The goal of this section is to outline the methods that can be used to predict the important thermodynamic
properties of the Nytrox oxidizers such as specific heats, densities and mole fractions in the liquid and
vapor phases at a selected state specified by a combination of pressure and temperature. For equilibrium
mixtures, for which this paper will be limited to, this task can be achieved by using the methods of classical
thermodynamics, specifically by the implementation of an Equation of State (EOS) with a mixing rule.
The details of the calculation process are outlined in the Appendix. Even though due to its relatively simple
form and reasonable accuracy, the Peng-Robinson EOS4 has been selected for the calculations discussed in
this paper, the use of a more accurate EOS is recommended for detailed design purposes. Some of the
important results from equilibrium thermodynamic calculations are discussed in the following paragraphs.
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The equilibrium phase data for the oxygen-nitrous oxide mixtures has been reported in Ref. 2 and 3 over a
limited range of temperatures. Zeinenger2 lists vapor and liquid mixture data for temperatures in the -60 C
to 20 C range, whereas Bracken et al.3 reports results for temperatures between -30 C and 30 C. Both data
sets have been used in this study to determine the variation of the mixture interaction parameter, k12, as a
function of temperature. As an example, for the O2/N2O system at -30 C, the mole fractions of oxygen in
the liquid and vapor phases have been calculated using the Peng-Robinson EOS and plotted in Figure 3.
The phase equilibrium data from Bracken et al. has also been included in the figure. The fit for the liquid
branch is excellent, whereas the predicted oxygen mole fractions in the vapor phase are lower than the
measured data. However, it is clear that even in the vapor phase, the error bounds are small and are
expected to be close to the accuracy level of the experimental data. The Peng-Robinson interaction
parameter that gives the best fit at this particular temperature is determined to be 0.0819. The deviation
from an ideal mixture (which requires an interaction parameter of zero) is small but finite.
Figure 3: Oxygen mole fraction as a function of pressure at -30 C. Data is from Ref. 3.
The process described in the previous paragraphs has been repeated for all of the data at varying
temperatures as they are reported by Zeinenger and Bracken et al. The interaction parameter, k12, values
obtained as a best fit to the experimental data has been plotted as a function of temperature in Figure 4.
Using standard analysis and curve fit techniques, it has been determined that the data given by Bracken et
al. is more reliable than the Zeinenger data and the k12 fit used in the calculations have been based on the
Bracken et al. data in the temperatures ranging from -30 C to 30 C. For temperatures between -30 C and 60 C the values obtained from the Zeinenger data has been used. Note that other than the 20 C case, the k12
values obtained from two data sets are in reasonably good agreement. The exact form of the k12 curve is
governed by the change of intermolecular interactions with temperature and the observed convex shape is
consistent with the results reported for other mixtures such as methane/decane5.
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Figure 4: Peng-Robinson parameter estimated from data reported in Refs. 1 and 2.
In the following section the important performance parameters for Nytrox oxidizers, which are predicted
using the methods developed in this section and the Appendix, will be presented.
VI) Performance of Nytrox Oxidizers
Figure 5 shows the liquid densities estimated for the O2/N2O mixtures as a function of pressure at different
temperatures. As a reference the liquid densities for pure substances (N2O and O2) are also included in the
figure. Note that for pure O2 and N2O, each point on the liquid density pressure curve is associated with a
different temperature, since for a two phase, single component system Gibb’s phase rule dictates that a
single intensive variable uniquely establishes the state of the substance. On the contrary since Nytrox is a
two component and two phase system, two intensive properties are needed to uniquely determine the state.
This expands the one dimensional operational space (saturation line) that exists for a pure substance to a
wide area (two dimensional) in the P-T diagram for the case of Nytrox. Note that all of the states enveloped
by Nytrox at its freezing temperature (-90 C or lower) and the N2O saturation line are feasible.
The most important observation from Figure 5 is that at a selected self-pressurization level, the densities of
the O2/N2O mixtures are significantly higher than the densities of the pure substances. The other important
observation is that for the O2/N2O mixture at a given temperature, the liquid density is not sensitive to the
system pressure as long as the pressure is not close to the critical value at that temperature. This feature of
the O2/N2O mixture gives the designer the flexibility of selecting the system pressure without affecting the
liquid oxidizer density significantly.
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Figure 5: Liquid density as a function of pressure at various temperatures for the O2/N2O mixtures.
Figure 6 shows the mass fraction of oxygen in the mixture as a function of pressure for various
temperatures. The general trend is that the oxygen mass fraction in the liquid increases with increasing
pressure and decreasing temperature. As shown in the figure, at 60 atm and -60 C, oxygen constitutes
approximately 15% of the liquid mass.
Figure 6: Oxidizer mass fraction in the liquid as a function of pressure at various temperatures for the
O2/N2O mixtures.
The specific impulse and c* performance of the O2/N2O mixtures at different oxygen concentrations have
been calculated using a thermochemical equilibrium calculation program. All calculations were conducted
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using paraffin as the fuel. The chamber pressure is 34 atm (500 psi), the nozzle area ratio is 70 and the
ambient pressure is zero.
The results are shown in Figure 7 and 8 for specific impulse and c*, respectively. The data for pure
oxidizers, liquid oxygen, N2O4 and N2O, are also included for reference. It is important to note that the 35%
O2/N2O mixture matches the Isp performance of N2O4. The other interesting observation is that even at low
oxidizer concentrations (such as 10%) the performance benefit and the shift in the optimal O/F is
significant.
Figure 7: The specific impulse performance for the mixtures of O2/N2O.
Figure 8: The c* performance for the mixtures of O2/N2O. The data is shown in uniform 10% increments
of the O2 mass fraction in the mixture.
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Figures 9 show the maximum Isp as a function of the oxygen mass fraction. Note that the O2/N2O mixture
with oxygen mass fraction that matches the inherent oxygen mass ratio of the N2O4 molecule outperforms
N2O4 due to the negative heat of formation of the dinitrogen tetroxide molecule. Also note that the optimum
O/F (for maximum Isp) decreases as the oxygen concentration in Nytrox increases.
Figure 9: The maximum Isp as a function of the mass fraction of oxygen for the mixtures of O2/N2O.
The performance of the equilibrium mixtures of O2/N2O is best summarized by Figures 10 and 11, which
show the plots of specific impulse and density impulse as a function of pressure at various temperatures.
Note that the specific impulse plot follows the oxidizer mass fraction trend given in Figure 6 as expected.
The density impulse which is a product of density and specific impulse follows the general trend of density,
since the variation of the density dominates the moderate changes in Isp for the range plotted in Figure 10.
Figure 10: Specific impulse as a function of pressure at various temperatures for the O2/N2O mixtures.
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Figure 11: Density impulse as a function of pressure at various temperatures for the O2/N2O mixtures.
The most critical observation from Figure 11 is that the density impulse of the cryogenic LOX system (at
14.7 psi of vapor pressure and 90 K of temperature) is almost matched by the O2/N2O mixture at -80 C and
60 atm of vapor pressure. The elimination or minimization of the external pressurization system and the
higher temperature operational capability would favor the O2/N2O mixture for a wide range of applications
where good performance, low cost and operational simplicity are critical.
Figure 12: Specific impulse as a function of oxidizer temperature for O2/N2O mixtures operating at a
pressure of 60 atm. Nozzle area ratio 70, shifting equilibrium, chamber pressure is 34 atm.
Finally as an example case, the performance of an O2/N2O system operating at 60 atm has been calculated
for various temperatures. The results are shown in Figures 12 and 13. As indicated in Figure 12, a system
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operating at -60 C has approximately 10 seconds of Isp advantage over the pure N2O system. More
remarkably the system has almost 70% improvement in the density impulse over the pure N2O oxidizer
(see Figure 13).
Figure 13: Impulse density as a function of oxidizer temperature for O2/N2O mixtures operating at a
pressure of 60 atm.
Figure 14: Regression rate as a function of the mass fraction of oxygen in the mixture. The regression rate
estimated using the classical theory arguments and normalized with respect to the regression rate of pure
N2O.
Classical hybrid rocket combustion theory as developed by Marxman et al.6 has been applied to predict the
effect of the oxygen mass fraction on the regression rate for a generic solid hydrocarbon fuel. The results
are plotted in Figure 14. Note that an increase of 29% in the regression rate is predicted by the classical
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theory as the mass fraction of O2 is increased from 0% to 100%. Note that this is a very crude prediction
and the regression rate law needed for the detailed design process should be developed from subscale motor
testing.
VII) Safety Advantages of Nytrox Oxidizers
Similar to hydrogen peroxide (H2O2) or hydrazine (N2H4), nitrous oxide can be regarded as a
monopropellant since its decomposition reaction is exothermic in nature7. The ignition of nitrous oxide (in
the vapor phase) can take place homogenously when the material is uniformly heated to a temperature
larger than its autoignition temperature (approximately 880 K) or locally when enough energy (or free
radicals) is locally introduced to the vapor at lower temperatures such that a self sustaining deflagration
wave (flame) can start to propagate in the medium8. Local thermal ignition is the most common failure
mode observed in rocket propulsion applications, since it is rather difficult to heat large quantities of
nitrous oxide to the auto-ignition temperature within the short periods that the rocket operation takes place.
Nitrous decomposition events have commonly been observed in the testing of rocket motors.
A particularly dangerous mode of failure is the decomposition of the N2O vapor in the oxidizer tank. Due to
the large quantities of N2O in the tank ullage, a decomposition process in the tank could potentially produce
large explosions resulting in injury to personnel and/or major hardware loss. Unfortunately at larger scales
the situation gets worse since the surface to volume ratio reduces as the tank size grows. This is especially a
problem for propulsion systems with closely coupled oxidizer tank and combustion chamber. For such
systems, at the end of the liquid burn, the hot injector could potentially heat the nitrous vapor in its vicinity
and start a deflagration wave that could propagate in the tank. Note that for pure nitrous oxide in a closed
vessel at 300 K, complete decomposition could result in a 24 fold increase in the tank pressure (a number
much larger than the safety factor of all flight tanks and most run tanks used for ground testing). This
indicates that even a partial decomposition could lead to a structural tank failure and loss of mission.
The safety advantage of Nytrox over N2O comes from the dilution effect of O2. Note that the vapor phase
of the Nytrox system has a large O2 concentration, in the range of 50-90 % by mass (i.e. see Figure 3). The
minimum energy to start a self sustaining deflagration wave in nitrous oxide with varying initial
concentration of oxygen is shown in Figure 15 for three initial pressure levels 40, 50 and 60 atm. Note that
the calculations are conducted assuming a spherical ignition kernel for a N2O/O2 gas mixture. As indicated
in the figure, a Nytrox system, even at a relatively low oxygen concentration of 35% by mass in the vapor
phase, requires more than 4,000 times more ignition energy compared to pure nitrous oxide. In summary,
Nytrox vapor is practically impossible to ignite with any ignition source that might exist in the tank. The
figure also shows that the effect of pressure is small (at the high pressure levels relevant to rocket
applications) compared to the effect of dilution.
Nytrox also presents some significant safety advantages compared to liquid oxygen due its reduced
cryogenic and fire hazards. The safety advantages of Nytrox oxidizers are expected to reduce the
development, recurring and operational costs associated with the propulsion system.
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Figure 15: Minimum ignition energy for N2O/O2 mixtures at three pressure levels.
VIII) Systems Advantages of Nytrox Oxidizers
In this section we summarize the results of a systems study that has been conducted to quantify the
performance advantages of Nytrox over the traditional oxidizers liquid oxygen and nitrous oxide. The
performance of several hybrid rocket concepts using different oxidizers have been calculated by matching
their total impulses to a baseline solid rocket. In order to directly compare the performance capability of the
hybrids to a modern operational solid, ATK’s GEM40 motor has been selected as the reference system with
the following properties.
Property
Gross Mass,
kg
GEM40
13,080
Structural
Mass
Fraction
0.10
Vacuum Isp,
sec
Length, m
(in.)
Diameter, m
(in)
Nozzle Area
Ratio
274.0
13.0 (511.8)
1.02 (40.0)
10.65
In the design process the following parameters are matched to their values for the GEM40 system:
Total Impulse: 3,162,107 N-sec
Outside Diameter: 1.02 m (40 inches)
Burn Time: 63.3 sec
The gross mass and the overall length of the hybrid systems are left free to change to meet the desired
performance requirements. Several hybrid options have been considered in the study for comparison
purposes:
1) N2O/paraffin with 20% aluminum powder by mass: This relatively low performance, yet
commonly used oxidizer has been included in the trade space as a reference point. Even though
N2O can be stored for extended durations at room temperature, it still requires thermal
management since the vapor pressure and the density are highly sensitive to temperature
variations. The aluminum concentration in the fuel is limited to 20% in order to keep the recurring
costs low and to minimize two phase losses in the nozzle.
2) Nyrox60/ paraffin with 20% aluminum powder by mass: The temperature of this particular grade
of Nytrox is -60 C.
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3) Nyrox80/ paraffin with 20% aluminum powder by mass: The temperature of this grade of Nytrox
is -80 C.
4) LOX/paraffin: Even though this is a high performance system, the cryogenic nature of the oxidizer
requires the use of metal tanks which compromises most of the performance gains associated with
its high Isp. The operations with this cryogenic material are expected to be much more
complicated and expensive compared to the other oxidizers. Fuel is straight paraffin, since
aluminum addition does not increase the specific impulse performance for high energy oxidizers
such as oxygen.
Note that only nontoxic, environmentally green, low cost, chemically stable and readily available oxidizers
have been considered in this investigation. For all systems other than the N2O motor which operates in the
blow down mode, the oxidizer mass flow rate is assumed constant.
All of the hybrids included in this study are pressure fed systems and the design details of the
pressurization system on the system performance are critical. The N2O is a self-pressurizing oxidizer at
room temperature and does not require any external pressurization hardware. This description is smowhat
misleading since at the end of the liquid burn, the vapor in the tank constitutes 10-15% of the total oxidizer
mass. In most system studies conducted with N2O a vapor phase combustion process is included in the
estimation of the total impulse. However sustaining stable and efficient combustion during the vapor phase
of the operation is problematic due to the sudden shift in the mass flow rate and consequently oxidizer to
fuel ratio during transition process from the liquid phase operation to the vapor phase operation. SPG’s past
motor testing experience with blow-down N2O motors indicates that the vapor phase combustion is either
not sustainable (sudden extinction of the flame at the moment of transition to vapor) or it is highly unstable
and inefficient. For this reason in the present system study, the vapor phase combustion is not allowed and
the contribution of the remaining mass at the end of the liquid burn to the total impulse is assumed to be
due to the expulsion of the cold N2O vapor. This feature makes the N2O systems quite inefficient, since, in
effect, the pressurization is achieved by a heavy noncombustible gas (N2O vapor itself). The weight savings
associated with the lack of extra pressurization hardware is also partially eliminated since the oxidizer tank
size has grown significantly (tank contains the liquid oxidizer and also the incombustible pressurant
generated from the liquid through evaporation).
The LOX-based system is the other extreme for which all of the pressurization is supplied by a foreign gas.
In this case helium is used to minimize the weight of the pressurant gas. As shown in Table 2 helium
constitutes a very small fraction of the overall system mass (0.82%). Its contribution on the total impulse,
which is also quite small, is produced in the cold gas thruster mode.
The pressurization situation with Nytrox oxidizers is interesting. As mentioned before, Nytrox systems are
partially self-pressurized. They start at high pressures but in the blow down mode they lose pressure at a
fast rate, since oxygen is expected to come out of solution rather slowly. Thus they require a supplementary
pressurization system. This can be achieved either by helium or gaseous oxygen. The advantage of helium
is its lightness. However helium is a limited natural resource and it has become quite expensive and
inaccessible in recent years. This trend is expected to get worse in the upcoming years.
The other alternative is to use gaseous oxygen as the supplementary pressurant for the Nytrox systems. For
such a system, at the end of the liquid burn most of the vapor is composed of oxygen (typically more than
90%). Note that the optimal oxidizer to fuel ratio (in terms of c*) for the oxygen paraffin system is around
2.2 as opposed to 7.5 in the case of N2O. As discussed above, the sudden reduction of oxidizer flow rate in
transition to the vapor phase, which results in a significant drop in the oxidizer to fuel ratio, is ideal for an
oxygen/paraffin hybrid. It is expected that the combustion process in this GOX hybrid operating close to its
optimum O/F can be sustained much more readily than the combustion with the N2O vapor (also note that
oxygen is a much more energetic oxidizer). Past experience with GOX/paraffin hybrids indicates that the
gas phase operation would be stable and efficient. Based on these arguments, in the calculations with
Nytrox systems, we have assumed that the gas phase combustion contributes significantly (more that 4% as
sown in Table 2) to the total impulse.
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Table 2: Summary of the performance parameters for the hybrid systems considered in the study.
System
N2O/20% AlNytrox60/20%
Nytrox80/20%
LOX/Paraffin
Paraffin
Al-Paraffin
Al-Paraffin
Gas Phase Impulse,
2.50
4.54
4.33
0.38
%*
Gas Phase Mass,
12.69
5.32
5.12
0.82
%**
Oxidizer Temperature,
22
-60
-80
-183
C
Oxidizer Tank
Al. lined
Al. lined
Al. lined
Al. 2219
Material
Graphite-epoxy
Graphite-epoxy
Graphite-epoxy
Oxidizer Specific
0.750
1.130
1.180
1.140
Density
Pressurization
O2-pressurized
O2-pressurized
Self-pressurized
He-pressurized
Scheme
partial
partial
Oxidizer to Fuel Ratio
6.0
5.0
5.0
2.7
Chamber Pressure, atm
40.8
40.8
40.8
(psi)
(600)
(600)
(600)
Liquid Isp,
271.3
278.4
279.8
sec
Effective Isp,
237.5
274.3
275.8
sec
Structural Mass
0.133
0.102
0.100
Fraction
Propulsion System
15,650
13,086
12,987
Mass***, kg
Increase in Mass,
19.7
0.0
-0.7
%
* Percent of total impulse, ** Percent of gross mass, ***GEM40 gross mass is 13,080 kg
40.8
(600)
306.8
304.8
0.200
13,233
1.2
The systems calculations have been conducted using SPG’s hybrid vehicle design code. Since the
complicated mission requirements have been replaced by the simple total impulse requirement on the
propulsion system, the flight modules have been disabled. The structural mass fraction is estimated within
the code using the preliminary design equations for the major components such as the oxidizer tank,
combustion chamber, pressurization system and nozzle. Available mass data have been used for small
components such as valves, regulators and ignition system. A mass margin of 15% has been added to the
calculated structural mass. The code outputs all the relevant performance, weight and geometrical
parameters which are summarized in Tables 2-4 for all systems considered in this study.
The oxidizer tank material for the LOX-based system is selected to be aluminum 2219. For all other
systems (which are not cryogenic), the tanks are made out of aluminum lined graphite-epoxy composite
material. The combustion chambers are also made out of graphite-epoxy composite with polymeric liners.
For the cryogenic LOX system an insulation thickness of 1.27 cm (0.5 inches) has been used. For both
Nytrox systems the thickness is assumed to be 0.64 cm (0.25 inches). Note that for all systems the outside
diameter of the insulation is matched to the GEM40 diameter of 1.02 m (40 inches).
In order to simplify the fabrication process and minimize the fuel sliver fraction, all motors are designed to
use a single circular port fuel grain. The initial to final diameter ratio for the fuel port is taken to be 2.0 to
limit the port Mach numbers and the hoop stresses on the port surface due to internal pressure loading. The
thickness of the motor insulation liner is 0.64 cm (0.25 inches) for all systems. A fuel sliver thickness of
0.25 cm (0.1 inches) has been assumed at the end of the burn (liquid and gas when possible). This
corresponds to fuel utilization of approximately 97% which has been successfully demonstrated in paraffinbased hybrid motor testing. The nozzles are made out of ablative silica phenolic inner shell and a structural
outer shell made out of glass phenolic. The nozzle erosion rates are extrapolated from actual motor test
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American Institute of Aeronautics and Astronautics
data. An erosion rate of 0.1524 mm/sec (0.006 in/sec) has been assumed at the reference chamber pressure
of 34.0 atm (500 psi). A linear variation for the erosion rate is assumed with the chamber pressure.
Moderate variations in the erosion rate are not expected to affect the system performance significantly. For
all systems the c* and nozzle efficiencies are assumed to be 0.96 and 0.98.
Even though the chamber pressure for the GEM40 system is 55.6 atm (817 psi), the hybrid systems have
optimized at a lower average pressure of 40.8 (600 psi). Note that this is due to the pressure independent
regression rate behavior, which is a key advantage of hybrids compared to solids. Since chamber pressure
can be selected independent of the internal ballistic considerations, more effective optimization is possible
(essentially one of the constraints is lifted).
Despite their reduced chamber pressures, all systems with the exception of the N2O motor deliver a better
Isp than the GEM40 system (listed vacuum Isp for GEM 40 is 274.0 sec). The structural mass fraction of
LOX system is quite high at 20% due to the use of aluminum tank material. The structural mass fraction for
the Nytrox systems is similar to the value for the GEM40 system (10%). This is mainly due to the fact that
the hybrids are optimized at a significantly reduced pressure. The structural mass fraction for the N2O
system is higher than the values for the Nytrox motors primarily due to the low density of this oxidizer.
The propulsion system weights for all systems are listed in Table 2. All systems other than N2O are close to
the weight of the GEM40 motor. In fact the Nytrox 80 system is 0.7% lighter. Note that the N2O system is
almost 20% heavier.
The weight distribution for the major components is shown in Table 3. The important observation is the
high tank weight for the LOX system. Also note that the weight increase in the tank weight for the N2O
system compared to the Nytrox systems is much larger than the weight of the pressurization system for the
Nytrox motors.
Table 3: Summary of the component masses for the hybrid systems considered in the study.
System
N2O/20% AlNytrox60/20%
Nytrox80/20%
LOX/Paraffin
Paraffin
Al-Paraffin
Al-Paraffin
Propulsion System
15,650
13,086
12,987
13,233
Mass, kg
Structural Mass,
2,077
1,335
1,298
2,657
kg
Tank Mass, kg
951
429
410
1,366
Chamber Mass, kg
Pressurization System
Mass*, kg
Nozzle Mass,
kg
*Excluding gas mass
282
283
282
426
0
79
76
98
160
164
164
170
The overall lengths of the hybrid systems along with other important geometrical data are listed in Table 4.
Note that all systems are longer than the GEM40 solid due to the low effective density of the hybrid
propellants. The N2O based booster is almost twice as long as GEM40 which makes it an unpractical
system. The shortest of all the systems considered in this study is the Nytrox80 based booster, around 40%
longer than GEM40. Nytrox60 and LOX based systems also have manageable length increases (less than
52%) over the baseline GEM40 booster. Note that for all systems, the motor outside diameter is matched
closely to the tank diameter, a virtue which can only be achieved with fast burning fuels for single port
hybrids. Hybrid configurations considered in this study are shown in Figure 16.
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American Institute of Aeronautics and Astronautics
Table 4: Summary of the dimensions for the hybrid systems considered in the study.
System
N2O/20% AlNytrox60/20%
Nytrox80/20%
LOX/Paraffin
Paraffin
Al-Paraffin
Al-Paraffin
Initial Nozzle Area
11.8
11.8
11.8
11.8
Ratio
Effective Nozzle
10.2
10.8
10.8
10.8
Area Ratio
Tank Diameter, m
1.02
1.00
1.00
0.99
(in)
(40.0)
(39.5)
(39.5)
(39.0)
Motor Diameter, m
0.96
0.99
0.99
1.00
(in)
(37.8)
(39.1)
(39.0)
(39.5)
Overall Length, m
25.78
18.84
18.24
19.69
(in)
(1015.0)
(741.6)
(718.2)
(775.0)
Length Increase*,
98.3
44.9
40.3
51.4
%
* Length of the GEM40 system is 13.0 m (511.8 inches).
Figure 16: Hybrid configurations for GEM40 replacement.
Even though the Nytrox-based hybrids are expected to be larger in size compared to the solids, their
throttling, safety and potential cost advantages make them superior to the solid rocket systems for a wide
range of applications. This fact has been demonstrated with the GEM 40 replacement study discussed in
this section.
There are also critical advantages of using Nytrox over LOX which do not directly influence the systems
performance but affect the cost and reliability of the system. Some of these can be listed as
•
The replacement of a cryogenic propellant with a cold liquid reduces the system and life cycle
cost and increases the reliability. Note that a respectable number of the system failure modes are
associated with the use of cryogenic propellants. For example cryogenic valve failures have
been commonly observed in rocket systems. Also note that cryogenic feed system components
are significantly more expensive.
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American Institute of Aeronautics and Astronautics
•
•
•
The cryogenic propellants constantly boil in the tank and they must be topped off (or actively
refrigerated) until the moment of launch. This is an expensive operation for ground launch
applications. For air launch systems cryogenic propellant management is even more difficult
and hazardous.
Due to the exothermic nature of the N2O decomposition process and warmer temperature of the
Nytrox oxidizer, the development of stable and efficient combustion systems is expected to be
less difficult with the Nytrox oxidizers compared to the cryogenic oxidizers. The injector design
would also be simpler for the same reasons.
There is a wide range of state properties (liquid density and oxygen mass fraction) that can be
realized by selecting the temperature and pressure of the Nytrox system. This feature allows the
designer to optimize the oxidizer for a given application. For example, higher oxygen
concentrations and densities might be desirable for certain applications where the lower
temperature operation would be acceptable.
The systems advantages of Nytrox over N2O are primarily due to its higher specific impulse and density.
Secondary effects such as safety and enhanced possibility of efficiently burning the gas phase would also
add value to Nytrox.
Even though this study is limited to a GEM 40 replacement hybrid, it is expected that there are many other
systems that would benefit from the use of Nytrox. Moreover even for the system considered in this study,
a full optimization on the Nytrox temperature and pressure has not been conducted. A much more detailed
system study that would quantify the advantages of Nytrox over a wider range of applications including a
more through optimization process would be beneficial for a better comparison of systems.
Nytrox oxidizers are perfectly applicable to liquid systems and they are expected to result in benefits
similar to the ones demonstrated for hybrids. In order to demonstrate this fact, a comparison of LOX/RP1
and Nytrox80/RP1 systems is shown in Table 5. Note that the Nytrox system is more than 10% denser than
the LOX based system. The density benefit along with the reduction in the tank weight (use of composite
materials), tank insulation weight and pressurization system weight would make the Nytrox stage lighter
and smaller compared to a LOX stage. Thus an all Nytrox vehicle would be significantly lighter and
smaller for a selected payload and target orbit compared to the baseline LOX system.
Table 5: Density Comparison - Liquid Systems.
Oxidizer to Fuel Ratio
Oxidizer Density, kg/m3
Fuel Density, kg/m3
Propellant Density, kg/m3
LOX/RP1
2.7
1,140
810
1,027
Nytox80/RP1
7.0
1,200
810
1,132
IX) Variations of Nytrox Oxidizers
As discussed in detail in the previous sections, the most basic version of the Nytrox technology uses the
equilibrium liquid mixtures of N2O and O2 as the oxidizing component of the propellant. This system is
composed of a liquid mixture and vapor mixture in phase equilibrium. The phase equilibrium determines
the oxidizer tank pressure and oxidizer density for a selected combination of temperature and oxidizer
concentration in the mixture. Note that the temperature and pressure can be adjusted to obtain the best
oxidizer mass fraction, liquid density, specific impulse combination for the specific mission. In the
following paragraphs we discuss some of the important variations of the baseline version of Nytrox
oxidizers that could have some merit in certain applications.
The first variation is to employ the use of equilibrium gas mixtures of N2O and O2 as oxidizing component.
This is a single phase oxidizer which would be readily available from gas companies. The gas phase
mixtures of N2O and O2 are expected to have better density than pure O2 gas and better Isp performance
compared to pure N2O.
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American Institute of Aeronautics and Astronautics
The other possible variation is the non-equilibrium liquid mixtures of N2O/O2. These mixtures would
potentially have better performance than the equilibrium mixtures since more oxygen can be loaded into the
system at a given temperature. Non-equilibrium systems should be meta-stable for the short durations of
operation typical in most rocket propulsion applications. The safe storage period is expected to depend on
the extent of non-equilibrium and storage conditions. Potential shortcomings of the non-equilibrium
systems are the limitation on the storage duration and the potentially more complicated oxidizer fill
procedures.
Another variation of Nytrox is the equilibrium and non-equilibrium mixtures of oxygen and other oxides of
nitrogen such as N2O4 or MON (mixtures of nitrogen oxides). These mixtures exhibit similar density and
pressure characteristics as the baseline Nytrox system (mixture of N2O and O2) at higher temperatures. The
important shortcoming is their toxicity. Note that some of the mixtures with practical significance are
N2O4/O2, N2O/O2/NO, N2O/O2/O3 or N2O/O2/NO/O3. The addition of NO into the baseline Nytrox would
add some extra pressurization capability, enhance the Isp performance and improve the reactivity of the
oxidizer. Addition of small quantities of ozone, O3 into baseline Nytrox would also be beneficial in terms
of enhancing the decomposition rate of nitrous oxide and the Isp performance, possibly improving motor
stability and efficiency.
In the simplest form of Nytrox, the pure N2O, N2O4 or MON oxidizer is pressurized by gaseous oxygen (in
the ullage). Note that in time some of the oxygen would be absorbed into the liquid oxidizer and eventually
the equilibrium composition at the corresponding temperature and pressure would be obtained. In this mode
of operation, the motor can be ignited well before the system equilibrates. The prime advantage of the
oxygen pressurization as opposed to the pure blow down system (pure N2O operating at room temperature)
or pressurization using an inert gas (i.e. He or N2) is that full combustion during the vapor flow stage of the
system operation (following the depletion of all the liquid in the oxidizer tank) is possible and the
pressurant gas contributes significantly to the total impulse increasing the efficiency of the overall
propulsion system.
Addition of other minor ingredients to control the chemical reactivity of the Nytrox formulations could also
be beneficial. As an example He could be added to reduce the sensitivity of Nytrox to chemical
decomposition or small amounts of organic or inorganic fuel component(s) can be incorporated to enhance
the reactivity of the baseline Nytrox. Addition of higher concentrations of fuels would result in a highly
sensitive but also a high performance monopropellant that could be beneficial for certain propulsion
applications. Note that the fuel component should be selected such that it would be highly miscible with
Nytrox but would have a low vapor pressure at Nytrox temperatures (to minimize the possibility of the
vapor phase explosion). The other types of additives that could prove to be beneficial are gelling agents.
X) Conclusions
The following is a summary of the important aspects of the Nytrox technology as it relates to rocket
propulsion applications.
•
•
•
•
•
•
Nytrox oxidizers are equilibrium or non-equilibrium mixtures of oxygen and nitrous oxide.
It has been shown in the medical literature that oxygen and nitrous oxide are perfectly miscible.
Significant quantities of oxygen can be dissolved in liquid nitrous oxide at low temperatures and
high pressures. The equilibrium mixtures are easy to prepare.
Nytrox oxidizers retain the practical advantages of its components.
Nytrox oxidizers have significant advantages over the pure components making them prime
candidates for hybrid and liquid propulsion systems.
The systems studies conducted for a GEM 40 replacement indicated that Nytrox systems have
significant weight and length advantages over systems using liquid oxygen or nitrous oxide
making hybrids a viable option for the existing solid rocket systems over a wide range of
applications.
No technical show-stoppers are anticipated in the development of Nytrox oxidizers. Preliminary
laboratory experiments and motor testing results are very promising.
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American Institute of Aeronautics and Astronautics
XI) Acknowledgements
I would like to thank my colleagues at SPG, Stanford University and NASA Ames for all of the stimulating
discussions that greatly helped mature the Nytrox technology. This work was supported by SPG’s IR&D
funds.
XII) References
1
Karabeyoglu A.,”Mixtures of Nitrous Oxide and Oxygen (Nytrox) as Oxidizers for Propulsion and Power
Generation Applications”, Patent Pending, Nov 2006.
2
Zeinenger H., “Flussikeits/Dampf-Gleichgewichte der Binaren Systeme N2O/N2, N2O/O2 und N2OCH4
bei Tiefen Temperaturen und Hohen Drucken”, Chem. Ing. Techn., Vol. 44, p 607, 1972.
3
Bracken A. B., Broughton G. B. and Hill W., “Equilibria for Mixtues of Oxygen and Nitrous Oxide and
Carbon Dioxide and Their Relevance to the Storage of N2O/O2 Cylinders for Use in Analgesia”, J. Phys.
D: Appl. Phys. 3, p. 1747-1758, 1970.
4
Peng Ding-Yu and Robinson Donald B., “A New Two Constant Equation of State”, Ind. Eng. Chem.
Fundam., Vol. 15 No. 1, 1976, p. 59-64.
5
Zudkevitch D. and Joffe J., A.I.Ch.E.J. 16, 112, 1970.
6
Marxman G. A., Wooldridge C. E. and Muzzy R.J., “Fundamentals of Hybrid Boundary Layer
Combustion”, Progress in Astronautics and Aeronautics, Vol.15, 1964 p 485.
7
Rhodes G. W., Investigation of Decomposition of Characteristics of Gaseous and Liquid Nitrous Oxide”,
Air Force Weapons Lab. Report no. AD-784802, Kirkland AFB, NM, 1974.
8
Karabeyoglu M. A., J. Dyer, J. Stevens and B. Cantwell, “Modeling of N2O Decomposition Events”,
AIAA-2008-4933, 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Hartford, CT,
July 21-23, 2008.
Appendix: Equilibrium Mixtures of Oxygen and Nitrous Oxide
It is critical to determine the properties of the equilibrium mixtures of oxygen and nitrous oxide in order to
quantify the performance benefits outlined in this paper. This requires the development of a state equation
for the mixture. The Peng-Robinson equation of state (EOS) which is given by Eq. 1 is widely used for
pure systems and mixtures due to its simplicity and higher accuracy (especially at high pressures) compared
to the other cubic EOS such as Soave-Redlich-Kwong equation.
P=
RT
a(T )
−
v − b v (v + b ) + b (v − b )
(1)
Here P, T, v are pressure, temperature and molar volume, respectively and R is the gas constant. Note that
the attraction parameter, a, is a function of temperature and the van der Waals covolume, b, is constant.
For most applications it is convenient to express Eq. 1 in the following cubic form.
Z 3 − (1 − B) Z 2 + ( A − 3B 2 − 2 B) Z − ( AB − B 2 − B 3 ) = 0
(2)
Here the coefficients A and B and the compressibility Z are defined as
A=
aP
2 2
R T
, B=
bP
Pv
and Z =
.
RT
RT
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American Institute of Aeronautics and Astronautics
(3)
Note that in the two phase region, the largest root of Eq. 2 corresponds to the compressibility of the vapor
phase whereas the smallest root is the compressibility of the liquid phase.
At the critical point the attraction parameter, van der Waals covolume and the compressibility become
a (Tc ) = 0.45724
R 2Tc2
RT
, b(Tc ) = 0.07780 c and Z c = 0.307 .
Pc
Pc
(4)
For all other temperatures the two coefficients can be written as
a (T ) = a(Tc ) α (Tr , ω ) and b(T ) = b(Tc ) .
(5)
Note that α is a function of the reduced temperature, Tr, and the acentric factor, ω, for the particular
molecule of interest.
α 1 / 2 = 1 + m(1 − Tr1 / 2 ) and m = 0.37464 + 1.54226ω − 0.26992ω 2
(6)
The reduced temperature is defined as
Tr =
T
.
Tc
(7)
The following parameters can be used for nitrous oxide and oxygen:
ω N 2O = 0.162
(Tc ) N 2O = 309.6 K
( Pc ) N 2O = 71.6atm
ωO 2 = 0.02 (Tc ) O 2 = 154.7 K
( Pc ) O 2 = 49.8atm
The fugacity, f, of a single component can be expressed as
A
 f 
 Z + 2.414 B 
ln  = Z − 1 − ln( Z − B) −
ln

P
 
2 2 B  Z − 0.414 B 
(8)
Note that at phase equilibrium, the fugacities of the liquid and the vapor should be matched.
fl = fv
(9)
Predicting the properties of equilibrium mixtures:
It has been determined that a single parameter (k12) binary mixing rule used in conjunction with the PengRobinson equation of state results in predictions that are in reasonably good agreement with the
experimental findings.
The following “mixture rule” which is recommended by Zudkevitch and Joffe5 is commonly used for
predicting the properties of non-ideal solutions of fluids as applied to the above EOS.
N
a=
N
∑∑ xi x j aij
i =1 j =1
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American Institute of Aeronautics and Astronautics
(10a)
N
b=
∑ xi bi
(10b)
i =1
aij = (1 − k ij )(ai a j )1 / 2
(10c)
Here xi refers to the mole fraction of the ith component. The interaction coefficient, kij, accounts for the
interaction between the molecules and it is typically experimentally determined. For an ideal solution, kij is
zero and deviation from zero indicates strong molecular interaction. In general, the interaction parameter is
a function of temperature and it typically takes a minimum value at an intermediate temperature value.
This fact has been demonstrated in Figure 4 for the N2O/O2 mixture but also has been observed for many
other mixtures such as methane/butane or methane/decane. The reason for the minimum is believed to be
due to the strong interaction in the liquid phase at low temperatures and strong interaction in the vapor
phase at high temperatures.
The fugacity of the kth component in the mixture can be expressed as
 N

2 x a

i
ik

 f k  bk
bk   Z + 2.414 B 
A  i =1
 ln
=
ln
( Z − 1) − ln( Z − B ) −
−
.

a
b   Z − 0.414 B 
2 2B 
 Px k  b






∑
(11)
Note that the equilibrium composition of the mixture can be obtained from the following condition for
equilibrium.
f kl = f kv
(12)
For binary mixture of oxygen and nitrous oxide the “mixing rule” reduces to
a = a O 2 xO2 2 + 2a12 x O 2 (1 − xO 2 ) + a N 2O (1 − xO 2 ) 2
(13a)
b = bO 2 xO 2 + b N 2O (1 − xO 2 )
(13b)
a12 = (1 − k12 ) (a O 2 a N 2O )1 / 2
(13c)
Example Case:
It is instructive to use an example to illustrate the method of determining the critical performance
parameters (such as Isp and impulse density) for the mixtures of oxygen/nitrous oxide as oxidizers. For the
purposes of this example, we arbitrarily select an initial tank temperature and pressure of -40 C and 60 atm,
respectively. Note that the density and oxygen concentration in the liquid phase are the two critical state
variables that are needed to estimate the propulsion system parameters. In order to obtain these state
variables, one can use a proven mixture rule and equation of state combination as discussed in the previous
paragraphs.
Assuming a desired pressure of 60 atm and a temperature of -40°C, Figure 5 can be used to read a liquid
density value of 1,070 kg/m3. Similarly, from Figure 6, the oxygen mass fraction in the liquid phase can be
determined to be 0.12. For this particular mixture, by using a standard thermochemical calculator (such as
NASA Glenn’s CEA program), one can calculate the maximum specific impulse for a selected fuel, nozzle
area ratio and combustion chamber pressure. Specifically for a paraffin-based fuel, a nozzle area ratio of
70, and a chamber pressure of 50 atm, a maximum specific impulse value of 327 s has been estimated.
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American Institute of Aeronautics and Astronautics