Technical ReportPDF Available

Preliminary design of a storable liquid propulsion system

Authors:

Abstract and Figures

The aim of the following report is to present a different set of solutions for a bi-propellant propulsion system of a 250 kg dry mass spacecraft’s kick-stage engine capable of performing a velocity variation of 2500 m/s. This analysis has been carried out considering two different propulsion couples. The first propulsion couple taken into account has been a toxic solution represented by hydrazine (N2H4) as fuel and nitrogen tetroxide (N2O4) as oxidizer. The second solution considered has been the green one based on kerosene (RP-1) as fuel and highly pure hydrogen peroxide (H2O2) with 98% concentration as oxidizer. Afterwards, an upscaling and downscaling study, for both the green and the toxic solution of the motor, has been performed, by doubling and halving the nominal thrust, but keeping the performance parameters constant . In the end, a discussion on the productive solution has been performed by analyzing the additive manufacturing possibility of realizing the kick stages obtained, considering also the adaptability of the selected material to this innovative process.
Content may be subject to copyright.
PRELIMINARY DESIGN OF A
STORABLE LIQUID PROPULSION
SYSTEM
Team ShipStar
Comi Luigi 10685455 luigi1.comi@mail.polimi.it
Corti Luca 10655314 luca10.corti@mail.polimi.it
Costantini Pietro 10750927 pietro.costantini@mail.polimi.it
Dalla Costa Thomas 10675136 thomas.dalla@mail.polimi.it
Di Bella Giuseppe 10660500 giuseppe1.dibella@mail.polimi.it
Ferrini Patrizia 10668541 patrizia.ferrini@mail.polimi.it
Garabelli Alfredo 10601137 alfredo.garabelli@mail.polimi.it
Locatelli Ludovica 10666520 ludovica.locatelli@mail.polimi.it
Course of Space Propulsion
A.Y. 2022-2023
September 13, 2024
Contents
1 Introduction 1
1.1 Background on kick stage rockets with storable liquid propellant . . . . . . . . 1
1.2 Study of a green alternative . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Way of reading the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Assumption and CEA code Analysis 5
2.1 Toxicpropellant................................... 5
2.2 GreenPropellant .................................. 7
2.3 Trade-ocomparison ................................ 9
3 Nozzle Design 9
3.1 Performances .................................... 9
3.1.1 Trade-off comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 RAOmodel ..................................... 10
3.2.1 Trade-off comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Combustion Chamber Design 11
4.1 Lassumption.................................... 11
4.2 Combustion chamber model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 Results........................................ 13
5 Injectors Design 14
5.1 Toxicpropellant................................... 14
5.2 Greenpropellant .................................. 14
5.3 Trade-ocomparison ................................ 15
6 Feeding Line Design 15
6.1 Toxicpropellant................................... 16
6.2 Greenpropellant .................................. 17
6.3 Tradeocomparison ................................ 18
7 Cooling Design 19
7.1 Thermalanalysis .................................. 19
7.2 Coolingstrategy................................... 20
8 Engine Upscaling and Downscaling 22
9 Additive Manufacturing 22
10 Conclusion 23
A Appendix A
CEA code I
A.1 Toxicpropellant................................... I
B.2 Greenpropellant .................................. II
I
B Appendix B
Nozzle Design III
A.1 Isoentropic and performance parameters equations . . . . . . . . . . . . . . . . III
C Appendix C
CC Design V
D Appendix D
Injectors VI
E Appendix E
Feeding line design VII
A.1 Pipes......................................... VII
B.2 Valves ........................................ VII
F Appendix F
Cooling design VIII
II
Abstract
The aim of the following report is to present a different set of solutions for a bi-propellant
propulsion system of a 250 kg dry mass spacecraft’s kick-stage engine capable of performing
a velocity variation of 2500 m/s.
This analysis has been carried out considering two different propulsion couples. The first
propulsion couple taken into account has been a toxic solution represented by hydrazine
(N2H4) as fuel and nitrogen tetroxide (N2O4) as oxidizer. The second solution considered
has been the green one based on kerosene (RP-1) as fuel and highly pure hydrogen peroxide
(H2O2) with 98% concentration as oxidizer.
Afterwards, an upscaling and downscaling study, for both the green and the toxic solution
of the motor, has been performed, by doubling and halving the nominal thrust, but keeping
the performance parameters constant .
In the end, a discussion on the productive solution has been performed by analyzing the
additive manufacturing possibility of realizing the kick stages obtained, considering also the
adaptability of the selected material to this innovative process.
III
Nomenclature
Symbol Definition Unit
αDivergent angle [deg]
AeExit area [m2]
AcCombustion chamber area [m2]
AtThroat area [m2]
βConvergent angle [deg]
CdDischarge coefficient
cFThrust coefficient
cCharacteristic velocity [m/s]
CC Combustion Chamber
conv Convergent
dinj Diameter of injector [m]
Dimp Distance of impinging point from the inj. plate [m]
DtDiameter of throat [m]
div Divergent
ϵArea Ratio
eEmissivity
ϵcContraction ratio
g0Gravitational acceleration at sea level (9.81) [m/s2]
H2O2Hydrogen Peroxide
hgConvective heat transfer coefficient [W/(m2K)]
H T P High Test Peroxide
IsSpecific impulse [s]
Ivac Specific impulse in vacuum [s]
KThermal conductivity [W/mK]
LSpecific length [m]
LcLength combustion chamber [cm]
Lconv Length of nozzle convergent part [m]
Ldiv Length of nozzle divergent part [m]
Ltot Total nozzle length [m]
MEOP Maximum Expected Operating Pressure [bar]
McMach number @combustion chamber
MeMach number @exit
˙mMass flow rate [kg/s]
˙minj Mass flow rate of injector [kg/s]
mprop Propellant mass [kg]
mfu Fuel mass [kg]
mox Oxidizer mass [kg]
MM H Monomethylhydrazine
MST Maximum Service Temperature
NNumber of injectors
N T O Nitrogen Tetroxide
N2ONitrous oxide
N2O4Dinitrogen tetroxide
(next page )
IV
( previous page)
N2H4Hydrazine
Nu Nusselt number
Dh Hydraulic diameter
Itot Total impulse [N s]
OF Oxidizer-fuel ratio
PaAtmospheric pressure [bar]
PcChamber pressure [bar]
Pcool Cooling jacket losses [bar]
Pinj Injector losses [bar]
PeExit Pressure [bar]
P r Prandtl number
QHeat flux [W]
qSpecific heat flux [W/m2]
RNozzle curvature radius [m]
Re Reynolds number
RP 1Green Fuel (kerosene)
TThrust [N]
Taw Adiabatic wall temperature [K]
tbBurning time [s]
Tcorr Corrosion Temperature [K]
Tdec Temperature of decomposition [K]
TcTemperature of combustion [K]
tres Residence time [ms]
Tfus Fusion Temperature [K]
Twg Wall gas side temperature [K]
TVariation of temperature [K]
veExit velocity [m/s]
vinj Injection velocity [m/s]
VcCombustion Chamber volume [m3]
Vprop Propellant volume [m3]
Vfu Fuel volume [m3]
Vox Oxidizer volume [m3]
ρDensity [kg/m3]
ρcPropellant density in the chamber [kg/m3]
λEfficiency of the divergent
γSpecific heat ratio
σStefan Boltzmann constant [W/(m2K4)]
θimp Angle of impingement [deg]
µDynamic viscosity coefficient [Pa s]
V
List of Figures
1.1 200N Bipropellant thruster by Ariane Group[12] . . . . . . . . . . . . . . . . . 2
1.2 Ideal mixture ratio & specific impulse values and compounds’densities[7] . . . 3
1.3 Performance evolution of 98%-HTP plus RP-1/Ethanol with respect to their
mixture ratios. Data produced by ArianeGroup internal performance code.[8] 4
1.4 Fuels vapor pressures at 25C........................... 4
2.1 Dependence of Tc/M on OF ratio in the T-kick . . . . . . . . . . . . . . . . . 6
2.2 Dependence of performance values on OF ratio in the T-kick . . . . . . . . . . 6
2.3 Dependence of temperature on OF ratio in the T-kick . . . . . . . . . . . . . . 7
2.4 Dependence of Tc/M on OF ratio in the G-kick . . . . . . . . . . . . . . . . . 8
2.5 Dependence of performance values on OF ratio in the G-kick . . . . . . . . . . 8
2.6 Dependence of temperature on OF ratio in the G-kick . . . . . . . . . . . . . . 8
2.7 Dependence of performance values on OF ratio comparison . . . . . . . . . . . 9
4.1 Shapiro analysis for combustion chamber pressure and Mach number variation 13
7.1 Specific heat flux trend along the CC and the nozzle (red) . . . . . . . . . . . 19
A.1 CEA code in toxic propellant case . . . . . . . . . . . . . . . . . . . . . . . . . I
A.2 CEA code in green propellant case . . . . . . . . . . . . . . . . . . . . . . . . II
B.1 RAO’s parabolic approximation for bell nozzle design . . . . . . . . . . . . . . IV
C.1 The characteristic length for different propellants . . . . . . . . . . . . . . . . V
D.1 DischargeCoecient ................................ VI
VI
List of Tables
1.1 Properties of the Hydrogen Peroxide at 20C[2].................. 3
1.2 Jet-A engine test’s results [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Constant parameters for CEA code analysis in the T-kick . . . . . . . . . . . . 5
2.2 Constant parameters for CEA code analysis in the G-kick . . . . . . . . . . . . 7
3.1 Performance parameter for the T-kick ...................... 10
3.2 Performance parameter for the G-kick ...................... 10
3.3 Geometric properties of the nozzle in the T-kick . . . . . . . . . . . . . . . . . 11
3.4 Geometric properties of nozzle in the G-kick . . . . . . . . . . . . . . . . . . . 11
4.1 Combustion Chamber design parameters in T-kick . . . . . . . . . . . . . . . . 13
4.2 Combustion Chamber design parameters in G-kick . . . . . . . . . . . . . . . . 13
5.1 injection plate parameters for T-kick . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 injection plate parameters for G-kick . . . . . . . . . . . . . . . . . . . . . . . 15
6.1 Main Values for Pressurizing Gas for T-kick . . . . . . . . . . . . . . . . . . . 16
6.2 Size of Helium tank for T-kick . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.3 Main Values for Fuel for T-kick . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.4 Main Values for oxidizer for T-kick . . . . . . . . . . . . . . . . . . . . . . . . 17
6.5 Size of Fuel tank for T-kick . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.6 Size of Oxidizer tank for T-kick . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.7 Main Values for Pressurizing Gas for G-kick . . . . . . . . . . . . . . . . . . . 17
6.8 Size of Helium tank for G-kick . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6.9 Main Values of Fuel for G-kick . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.10 Main Values of oxidizer for G-kick . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.11 Size of Fuel tank for G-kick . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.12 Size of Oxidizer tank for G-kick . . . . . . . . . . . . . . . . . . . . . . . . . . 18
7.1 HeattransferforT-kick .............................. 20
7.2 HeattransferforT-kick .............................. 20
7.3 C-103 main features ................................ 20
7.4 Cooling liquid temperature increase for T-Kick . . . . . . . . . . . . . . . . . . 20
7.5 Cooling liquid temperature increase for G-Kick . . . . . . . . . . . . . . . . . . 21
7.6 Radiative dissipated heat for T-kick . . . . . . . . . . . . . . . . . . . . . . . . 21
7.7 Radiative dissipated heat for G-kick . . . . . . . . . . . . . . . . . . . . . . . . 21
9.1 Additive manufacturing features of EOS M 400 Series ............. 23
10.1 final comparison between the T-kick and G-kick . . . . . . . . . . . . . . . . . 23
E.1 Values of 1/4” stainless steel pipe . . . . . . . . . . . . . . . . . . . . . . . . . VII
E.2 Values of Gas Pressure Regulator . . . . . . . . . . . . . . . . . . . . . . . . . VII
E.3 ValuesofCheckValve ............................... VII
E.4 ValuesofLatchValve................................ VIII
VII
1. Introduction
1.1 Background on kick stage rockets with storable liq-
uid propellant
In this modern space era, the target for space industries is the development of new technologies
in order to increase the versatility of launchers in performing a wide range of missions and
optimizing costs. The kick-stage is an optional additional stage that is able to refine the
orbit injection of spacecrafts or, more recently with the spread of microsatellite technologies,
deploy clusters of CubeSats satellites in their correct orbit (space tug).
Here is reported a list of some of the existing or in development kick stages[21][22]:
ASTRIS, by ArianeGroup, uses as propellant the storable couple MON/MMH, this
stage has been developed to extend the Ariane 6 versatility towards efficiency and op-
timized new missions. ASTRIS enables the direct placing of satellites in their geosta-
tionary orbits and facilitates missions to the Moon and deep space exploration also
reducing the transport time. This novel kick stage is intended to perform its first flight
by 2030.[20]
Orbiter, by Launcher, has a storable propellant composed of N2Oand ethane, it has a
payload capability of transporting up to 400 kg of small and microsatellites.[43]
Spaceflight Industries realised the Sherpa kick stage in different sizes. Sherpa LTC
uses a bi-propellant storable propulsion system, reaching up to 88 N (in total for all the
four motors); in addition, Sherpa 2200 works with the couple MMH/NTO reaching in
total 360 N of thrust. This kind of kick stages provide a low-cost, rapid orbital transfer
for many sizes of small spacecraft.[46]
Space Tug, by Skyrora, is based on the upper stage of the Skyrora XL launch vehicle.
The Space Tug will offer an abundance of environmental benefits: it allows multiple
payloads to be deployed into their chosen orbits from the same launch, minimising the
environmental impact of rocket launch by reducing the number of launches. It uses the
green couple HTP/Kerosene as propellant and allows up to 3.5 kN of thrust with a dry
mass of 530 kg.[45]
Rocket Lab’s kick stage provides flexibility for orbital deployment. It is powered by Curie
engine, an additively manufactured 120 N engine, that works with a green bi-propellant.
In its most advanced configuration the kick stage becomes Photon, a satellite bus
that supports several-year duration missions to LEO, MEO, Lunar and interplanetary
destinations [23][45].
For these kinds of applications, the most common propulsion system is a liquid storable bi-
propellant rocket engine system, in particular with the couple hydrazine, or its derivative,
as fuel, and nitrogen-tetroxide (N2O4)as oxidizer. The benefits of the couple are its high
specific impulse, its hypergolic nature and storage stability, while the main withdrawal is the
two components’ high toxicity. Different solutions have been developed for this kind of tech-
nology and many others are still in evolution taking into particular account green solutions
for the propulsive couple.
1
Figure 1.1: 200N Bipropellant thruster by Ariane Group[12]
Liquid propellant kick stage rockets are part of Ariane Group chemical propulsion systems
mainly flying in commercial GEO programs and recent science missions like Rosetta and Gaia
and future challenging missions like Bepi Colombo, Lisa Pathfinder and Solar Orbiter.
The 200 N bi-propellant engine was developed and qualified for application as attitude control,
maneuvering and braking thruster of ESA‘s ATV.
Using MMH and N2O4, the nominal thrust for this engine is around 216N , with a spe-
cific impulse at nominal point around 270s and a nominal chamber pressure around 8 bar.
[12]
1.2 Study of a green alternative
As we said in the section above, the NTO and the Hydrazine are extremely toxic, for this
reason, a possible green alternative can be presented.
These propellant technologies are increasingly being developed and adopted as a replace-
ment for common toxic propellants and include replacements such as the emerging ‘green’
ionic liquids, and more conventional propellants like hydrogen peroxide or electrolyzed water.
The advantages of using green propellants are:
higher specific impulse performance than the current state-of-the-art hydrazine mono-
propellant thrusters for similar thrust classes;
higher density specific impulse achieving improved mass fractions;
lower minimum storage temperatures, which may be beneficial in power-limited space-
craft;
lower tank and line heater requirements;
The disadvantages:
2
high catalyst pre-heating required;
higher combustion temperatures than hydrazine;
Current research worldwide considers hydrogen peroxide for propulsive application, using
mostly concentrations in the range of 87.5–98%, one of the favourite candidates to replace
hydrazine in monopropellant and bi-propellant systems, despite some downsides such as the
long-term storability or the low performances. The highest available HTP concentration, 98%
is chosen.
Oxidizers Chemical formula Molecular
weight
Freezing
point [c]
Normal boil-
ing point [c]
Density
[g/cm3]
HTP 98% 98%H2O2+ 2%H2O33.7 -2 148 1.437
Table 1.1: Properties of the Hydrogen Peroxide at 20C[2].
Three hydrocarbon fuels are evaluated in this trade-off to be used in combination with
98%-HTP:
Ethanol
Kerosene (RP-1)
Isopropanol
The choice of the fuel is based on many factors. From a cost perspective, Kerosene is almost
half as expensive as Ethanol, despite both being extremely affordable. [7]
At the optimum mixture ratio condition the 98%-HTP/Kerosene combination is more perfor-
mant than the 98%-HTP/Ethanol one, as seen in figure 1.2 and figure 1.3. [8]
Figure 1.2: Ideal mixture ratio & specific impulse values and compounds’densities[7]
Therefore, choosing RP-1 means that more HTP would be consumed in the combustion
process. An important consideration follows: 98%-HTP is about one hundred times more
expensive than Kerosene.
From a technical perspective, tests have already been conducted with Ethanol in the
framework of the FLPP Green Storable Propulsion project while no data are yet available
for Kerosene to support the trade-off. However, Kerosene is a well-known propellant and has
already been used in combination with HTP in the Black Arrow programme, Skyrora Tug
Stage, LunaNova Kick-Stage.[8]
The vapour pressure is an important parameter to consider when designing an engine.
As reported, all three fuels have vapour pressure values way below the foreseen Maximum
Expected Operating Pressure (MEOP) of 5 bar. No difference in storage and safety procedure
is therefore expected.
3
Figure 1.3: Performance evolution of 98%-HTP plus RP-1/Ethanol with respect to their
mixture ratios. Data produced by ArianeGroup internal performance code.[8]
Figure 1.4: Fuels vapor pressures at 25C
Another consideration should be done on performance impact on payload mass. Indeed,
since the 98%-HTP/RP-1 mixture shows a specific impulse 5s higher than 98%-HTP/Ethanol
or 98%-HTP/Isopropanol combinations, the same propellant mass has the capacity to carry
more payload.
Combustion of HTP/Hydrocarbon mixture usually requires an igniter or a catalytic pre-
decomposition of HTP. The ignition temperature is lower with RP-1 and might therefore offer
higher flexibility.[7]
In conclusion, Kerosene (RP-1) is chosen as fuel for these reasons:
Its higher Isenables a cheaper flight cost;
Its higher MR reduces the tank mass;
Its flatter Is(MR) curve provides more flexibility in tuning the MR to compensate the
drift of the stage centre of gravity as the propellant is consumed.[7]
This report focused on kick-stage rockets takes as landmark the studies developed by
LunaNova project, Skyrora Tug Stage and especially a bi-propellant engine project of the
Institute of Aviation Space Technologies Department (Poland) called Jet-A.
The interior project of the IoA has the goal to present the feasibility of developing a low-
cost, reliable, pressure-fed GEO satellite thruster using HTP and Hydrazine. Jet-A is being
used with 98% hydrogen peroxide of HTP class, showing acceptable, at this moment of devel-
4
opment, ignition lags (delay times). [3]
Many experiments of kerosene injection into decomposed HTP flow performed with a
chamber pressures between 2 and 15 bar, a low OF value of 3.4 and the autoignition of the
catalyst bed leds to following results :
OF PcIsreal Istheory TcTdec Thrust
3.4 11bar 1840m/s 1947.8m/s 2850K1200K270N
Table 1.2: Jet-A engine test’s results [3]
The described project allowed the development of a simple bi-propellant rocket engine
giving a specific impulse efficiency of over 94% which is a very good result for a small propul-
sion system, even if this result can be slightly too optimistic, due to the measurement system
utilized. [3]
1.3 Way of reading the report
In each chapter, are analyzed two different kick motors: one using a toxic propellant (MMH-
N2O4), the other a non-toxic (green) propellant alternative (HTP-RP-1). In order to make
the reading more fluent, from this point the toxic motor version will be called T-kick and the
remaining one, G-kick.
Moreover, the report described another distinction between the motors, it depends on the
scale. In fact, are analyzed, in addition to the nominal case (called M), other two types, which
differ from the nominal case because one has the Thalf of the nominal (called S) and the
other, the double (called L). This distinction is notable inside the tables of the values in each
chapter, in order to underline the differences between these alternatives.
2. Assumption and CEA code Analysis
2.1 Toxic propellant
Kick stage rockets are propulsion systems that operate out of the Earth’s atmosphere, for this
reason, the Pais set to zero. In order to begin the design of the motors, it is necessary to
make some hypothesis on missing data by looking at other existing examples from the litera-
ture:(consult 1.1)
T= 200N Pc= 8bar ϵ = 150 OF = 0.9
Table 2.1: Constant parameters for CEA code analysis in the T-kick
These assumptions are made following and analyzing a similar kick motor of the Ariane-
group. [4]
5
Once selected the Pcand ϵa CEA analysis is performed to select the oxidizer to fuel ra-
tio in order to optimize the combustion chamber temperature to molar mass ratio, as could
be seen in figure 2.1.
Figure 2.1: Dependence of Tc/M on OF ratio in the T-kick
The best performance value of the stoichiometric OF ratio (around 1.1) of the hydrazine/ni-
trogen tetroxide couple is not selected although, as shown in figure 2.2, c,Ivac and cFare
optimized by this stoichiometric value.
Figure 2.2: Dependence of performance values on OF ratio in the T-kick
The choice of picking a different value from the stoichiometric is driven by the high com-
bustion chamber temperature (shown in figure 2.3), which is too high for the wall thermal
resistance.
6
Figure 2.3: Dependence of temperature on OF ratio in the T-kick
The CEA code is used in order to obtain all the values useful for the thermochemical
analysis, assuming the Bray model. The equilibrium model is developed and used from the
entrance of the combustion chamber to the throat section while the frozen model is used after
the throat until the exit section of the nozzle. Instead, for the values of the nozzle performance
parameters, such as Isand cF, the isotropic expansion model implementation is preferred.
2.2 Green Propellant
The hypotheses made for the green propellant rocket design are the following:
T= 200N Pc= 8bar ϵ = 150 OF = 5.25
Table 2.2: Constant parameters for CEA code analysis in the G-kick
The choice of picking the same Pcand ϵis driven by the possibility of comparing the green
solution with the toxic one. The only variation from the case analyzed above is the OF ratio.
The choice of taking 5.25 as value is driven by the same consideration made in the toxic case
(Figure 2.4)
7
Figure 2.4: Dependence of Tc/M on OF ratio in the G-kick
In figure 2.5 and 2.6 are reported the graphs used to select the OF ratio for the green
alternative, following the same considerations adopted for the toxic case.
Figure 2.5: Dependence of performance values on OF ratio in the G-kick
Figure 2.6: Dependence of temperature on OF ratio in the G-kick
Also in this case the CEA code is used to obtain the values useful for the thermochemical
analysis, using the Bray model, but preferring the isentropic expansion model to compute the
8
nozzle performance parameters.
2.3 Trade-off comparison
Figure 2.7: Dependence of performance values on OF ratio comparison
The couple MMH-NTO generally has higher performances, but the action range is lower.
From figure 2.7 it is possible to notice that the performances of the toxic couple decay drasti-
cally from the stoichiometric point.
The opposite is for the couple HTP-RP1, which overall performances are lower, but the
trend is more uniform around the stoichiometric point.
3. Nozzle Design
The procedure used in order to compute the nozzle performances and carry out its design is
explained in this chapter. Despite the procedure used in order to derive the design parameters
being the same for both the toxic and green propellant, the input values are different and
produce different outputs.
The design of the nozzle is split into two parts: the first is the analysis of its performances,
and the second, performed after the CC design, is the computation of its geometrical charac-
teristics, using the RAO model.
3.1 Performances
The required data for the computation of the main performance parameters are the T,PC,Pa
and ϵ, in addition to some outputs of the CEA analysis.
Knowing the Pc,ϵand γvalue of the gas, it is computed Pe, inverting the equation B.1
using Matlab function X=fzero(FUN,X0). Once obtained the Pe, it is possible to calculate cF
from equation B.2.
Having now the value of the thrust coefficient, Pcand T,Atcan be derived. Moreover, using
ϵ, is obtained also the value of Ae.
The next step is to use the equation B.3 to compute ve, and from this value, inverting the
9
equation for non-optimal thrust, is calculated ˙m(equation B.4) and then Ivac from equation
B.5.
Finally, from the equation B.6, is derived Me, using again Matlab function X=fzero(FUN,X0).
The values obtained for the performance analysis are reported below.
The parameters unaffected by the sizing of the T-kick are:
cFc[m/s]Ivac[s]ve[m/s]Pe[bar]Me
1.790 1678.969 306.352 2961.707 1.385 1036.415
Table 3.1: Performance parameter for the T-kick
Only the mass flow rate differs with respect to the size of the toxic engine:
S M L
˙m [kg/s] 3.327 ·1026.655 ·1021.221 ·101
Also for the G-kick motor, the performance parameters remained unchanged are:
cFc[m/s]Ivac[s]ve[m/s]Pe[bar]Me
1.855 1567.094 296.366 2850.198 1.945 ·1035.699
Table 3.2: Performance parameter for the G-kick
Only the mass flow rate differs with respect to the size of the green engine:
S M L
˙m [kg/s] 3.438 ·1026.879 ·1021.376 ·101
3.1.1 Trade-off comparison
The toxic solution and the green one are not so different in terms of Ivac,veand ˙m. On the
other hand, the G-kick is characterized by a little advantage in terms of cF, in the face of a
higher Peand lower cand Me. Since Tand Pcare assumed equal for the two solutions, this
difference in the cFimplies a difference in the Atbetween the two solutions. The same can be
said for the difference in the values of c.
3.2 RAO model
The computation of the nozzle geometrical properties starts from the conical model, assum-
ing α= 15for the divergent wall and β= 45for the convergent (chosen from literature [10]).
The values of Atand Aeare reported in the subsection 3.1. Furthermore, from the value
of ϵc(see chapter 4) it is possible to derive Ac.
Knowing these values for the sections, it is possible to derive the length of the convergent and
divergent part of the nozzle and then, its total length.
The chosen approach for the RAO nozzle design is the minimum length approach with the
length of the divergent part equal to 60% of the length of the conical one and the same con-
vergent part.
10
The choice of the minimum length approach is reasonable because, operating with a kick stage
motor, the propulsion subsystem can’t occupy too much space while it is stored inside the
launcher, as payload, in the first phase of the mission; so this approach allows to save some
space.
With a graphical method from the RAO curves, as shown in figure B.1, it is possible to select
the initial and the final parabola angle (θi= 41.7and θe= 12.2respectively) of the divergent
wall. From these values, the new αis equal to 24.1and consequently the efficiency of the
divergent part (λ= 0.9860) can be computed.
The geometrical properties of the designed nozzle, in the case of a hydrazine-nitrogen
tetroxide (T-kick), using the RAO model, are reported in the following table:
Size At[cm2]Ae[cm2]Lconv[cm]Ldiv[cm]Ltot [cm]
S4.084 0.698 104.750 0.667 11.874 12.543
M8.167 1.397 209.500 0.946 16.793 17.738
L16.335 2.793 419.000 1.337 23.747 25.086
Table 3.3: Geometric properties of the nozzle in the T-kick
Table 3.3 shows that the sizing scale affects all the parameters for nozzle design.
For the G-kick motor case, that uses hydrogen peroxide and RP1, the geometrical prop-
erties are listed in the following table:
Size Ac[cm2]At[cm2]Ae[cm2]Lconv[cm]Ldiv[cm]Ltot [cm]
S3.967 0.674 101.064 0.661 11.663 12.324
M7.934 1.347 202.129 0.934 16.495 17.429
L15.869 2.695 404.258 1.321 23.327 24.648
Table 3.4: Geometric properties of nozzle in the G-kick
3.2.1 Trade-off comparison
The difference in the geometrical properties between the two nominal solutions is not so high,
bringing to a very similar shape for the two nozzles. The little differences obtained are caused
by the low variation of performance parameters between the green and the toxic case that
they are called to guarantee.
4. Combustion Chamber Design
The procedure used in order to design the combustion chamber is explained in this chapter.
Despite the procedure used is the same for both the toxic and green propellant, the input
values are different and produce different outputs.
4.1 Lassumption
One of the most important parameters that characterize the combustion chamber is the char-
acteristic length L, an experimental parameter which defines the proper volume of the
11
combustion chamber to assure the completion of the propellant’s combustion.
From the literature C.1, the N2H4- NTO propulsion system is characterized by a Lthat
varies from 30 to 35 inches. The choice made is 35 inches corresponding to 0.889 mand it is
driven by the usual values of residence time that a kick stage requires to complete the reaction
inside the CC.
On the other hand, due to the lack of information in the literature about the Lof the
selected green couple without the catalyst bed, following the reference C.1 the value varies
from 60 to 70 inches.
The choice made is 60 inches, corresponding to 1.524 m, taking a margin of 20% considering
the additional length of the combustion chamber needed to guarantee a complete reaction
between fuel and oxidizer also without a catalyst bed. The final value assumed for L, for the
green solution, is 1.829 m.
4.2 Combustion chamber model
Starting from L, ˙m,Atand some information from CEA analysis (among which the Tc) and
assuming Mc= 1 for the flow in CC, it is possible to start the design of CC.
To compute the value of the section of the CC, a Mach number (Mc) of 0,1 is imposed in
the combustion chamber, this value is lower than the theoretical limit of 0.6. Knowing the
chemical composition of the gas inside the CC and the adiabatic flame temperature, from the
CEA analysis it is possible to compute the speed of sound and consequently the velocity of
the gas.
Then, applying the continuity equation, knowing the mass flow rate of the propellant from
the nozzle performances, it is possible to compute the section of the combustion chamber and,
assuming a cylindrical shape, its length is derived.
Furthermore knowing the required parameters defining the residence time it is possible to
compute its value. The residence time value allows knowing if the time spent by the gas inside
the CC is enough to complete the reaction and the found value of 1.1 ms is good for our first
approximation.
To check the validity of the used model also the contraction ratio ϵcis computed. The value of
the contraction ratio ϵcfound is 5.8478, which is larger than usual values from the literature
but it’s still acceptable for small kick motors.[14]
Since Lof the green solution is different from the toxic one, the residence time obtained
is 2.6ms which is sufficient to assure the complement of the reaction in CC. Another change
can be noticed also in the value of ϵc, which value is slightly higher, equal to 5.8881.
12
4.3 Results
Size Pc[bar] Tc[K] tres [ms] Vc[cm3]Ac[cm2]Lc[cm]
S8 2847 1.1 62.082 4.084 15.202
M8 2847 1.1 124.164 8.167 15.202
L8 2847 1.1 248.327 16.335 15.202
Table 4.1: Combustion Chamber design parameters in T-kick
Size Pc[bar] Tc[K] tres [ms] Vc[cm3]Ac[cm2]Lc[cm]
S8 2730 2.611 123.218 3.967 31.059
M8 2730 2.611 246.435 7.934 31.059
L8 2730 2.611 492.871 15.869 31.059
Table 4.2: Combustion Chamber design parameters in G-kick
The combustion chamber of T-Kick M and G-Kick M are very different, especially for
what concerns the Lc. This difference is imputed to the thermochemical properties of the two
propellants. In fact, although the thermodynamical properties of the two nominal motors (Pc
and Tc) are very similar, the geometrical properties are different, especially Lcand so Vc(Ac
is not so different). The couple RP1-H2O2 is characterized by a Lmuch higher than the
N2H4-N2O4’s one, almost double. This variation is imputable not only to the hypergolicity
of the toxic couple but also to the choice of avoiding using a catalyst bed for the G-Kick,
with the aim of obtaining a liquid injection. The different Lhas driven to obtain a different
Vcfor the two nominal solutions that, since the Acare very similar, produce a much longer
combustion chamber for the nominal green solution with respect to the toxic one.
Finally is here represented a Shapiro analysis for the Mcand Pc(static) variation in the
combustion chamber both for toxic and green solutions for three different T(temperature
variation). In the analysis made in the previous section has been assumed a constant Mcof
0.1 and a constant Pcof 8 bar for the entire combustion chamber. This is good for preliminary
analysis, but in reality, the values of Mcand Pcchange along the combustion chamber: the
Mcis subjected to an increment, while the Pcdecrement.
Figure 4.1: Shapiro analysis for combustion chamber pressure and Mach number variation
13
5. Injectors Design
5.1 Toxic propellant
The injection plate is one of the most critical components in the design. The propellant is
one of the main drivers for the choice of the type of injector configuration. As Hydrazine and
N2O4are hypergolic propellants, they don’t require an ignition system and the choice of the
injector configuration fell on a self-impinging pattern, also because both fuel and oxidizer
are in a liquid state. Impinging injectors provide better mixing than a showerhead and are
simpler than swirling or coaxial injectors.
For simplicity, a one-to-one pairing between fuel and oxidizer injectors is chosen and the
geometry selected is as a short tube with a conical entrance, which provides a higher discharge
coefficient than other configurations. The Cdconsidered is taken from the literature with a
value of 0.7 D.1.
A pressure drop of 40% is chosen to provide a high enough exit velocity, from the injectors,
to favour the atomization.
To compute the number of injectors, an initial diameter is chosen, which takes into ac-
count the type of manufacturing technique and its limitation. Subsequently, the area of a
single injector is computed and the number of total injectors is found. To assure that the
number found is even, a check is conducted and if it failed a correction is made to have the
correct even number that makes it possible to find the real area of a single injector. This
procedure is conducted for both fuel and oxidizer injectors. To assure that the injection plate
is not overcrowded, a manual check is made on the number of couples found also comparing
this number with some models found in the literature [24][25].
The same impinging angle of 30°is selected both for the fuel and oxidizer. This choice is
driven by examples found in the literature and from dimensional constraints of the combustion
chamber [28]. Another parameter computed, thanks to the relation found in the literature,
is the vertical distance from the plate of the impinging point. Also, these values are
checked and found to be acceptable [27][30].
S M L
ox fu ox fu ox fu
N 2 2 2 4 6 8
˙minj [kg/s] 0.00788 0.00876 0.01576 0.00876 0.01051 0.00876
dinj [mm] 0.686 0.793 0.670 0.793 0.792 0.793
Dimp[mm] 3.430 3.963 4.850 3.963 3.960 3.963
vinj [m/s] 14.706 17.669 14.706 17.669 14.706 17.669
θimp[deg] 30 30 30 30 30 30
Table 5.1: injection plate parameters for T-kick
5.2 Green propellant
The designing process of the injection plate starts by assuming that the two propellants enter
the injectors in liquid form, neglecting in such a way the decomposition of the H2O2. This
strategy is less efficient than the use of a catalyst bed to decompose the oxidizer, however, for
14
this preliminary analysis, it is a good approximation.
Atriplet injector configuration with the fuel impinging on the oxidizer is chosen. The choice
of a triplet instead of a doublet is driven in order to provide a better mixing between the fuel
and the oxidizer.
The geometry of the injector is the same as the doublet, for the same motivation. As for the
hypergolic propellant injection plate, the pressure drop is a 40% to assure an injection velocity
high enough to provide good atomization.
As a first iteration to calculate the number of injectors, an initial diameter for the fuel injectors
is selected, this takes into account the type of manufacturing technique and its limitation.
Then the number of oxidizer injectors and their relative diameters are computed. A check on
the number of oxidizer injectors is made and, in case it is not an integer, it is rounded to the
lower integer. If it is the case, the number of the fuel injectors is recomputed and so is their
relative diameter.
Also, to assure that the injector plate is not overcrowded, a manual check is made comparing
it with a similar plate found in the literature [25][24].
As for the hypergolic propellant, the impinging angle for the fuel is chosen as 30 deg,
while for the oxidizer the impinging angle is 0. Another parameter that is computed, thanks
to relation in the literature, is the vertical distance from the plate of the impinging
point. Also, these values are checked and considered to be acceptable [26].
S M L
ox fu ox fu ox fu
N 1 2 2 4 3 6
˙minj [kg/s] 0.0289 0.00275 0.0289 0.00275 0.0385 0.00367
dinj [mm] 1.316 0.467 1.316 0.467 1.520 0.540
Dimp[mm] - 4.048 - 4.048 - 4.674
vinj [m/s] 14.773 19.556 14.773 19.556 14.773 19.556
θimp[deg] 0 30 0 30 0 30
Table 5.2: injection plate parameters for G-kick
5.3 Trade-off comparison
For both the toxic and green propellant all parameters of the injectors need to be checked
with CFD simulation and real-life testing, to assure a proper mixture of fuel and oxidizer and
proper structural integrity. Also, the disposition on the plate of the doublet and triplets must
be chosen to avoid flame instability. This last part is out of the scope of the assignment.
6. Feeding Line Design
The architecture chosen for the feeding line is a standard pressure-fed that involves different
tanks for pressurizing gas and fuel and oxidizer. The gas selected is Helium. Helium is used
because its normal boiling point is lower than that of hydrogen. Thus it can be used without
compromising propellant integrity or feed-system function. Other gases would freeze, produc-
ing particles that could clog equipment and seize an engine, or react with or dissolve in the
liquid hydrogen, reducing engine efficiency, all with potentially disastrous results. [8]
The system consists of a high-pressure gas tank, gas pressure regulators, two check valves, fuel
and oxidizer tanks and two latch valves. All the components are connected with pipes.
In order to design the feed line the distributed and concentrated losses are taken into account.
15
The length of the pipes is set with respect to the dimensions of the tanks, so, as a first approx-
imation, the distributed losses along the pipes are considered as the 3% of Pc; a 1/4” diameter
pipes is selected for standardization, market availability, lower cost and compatibility with the
valves.
The valves are taken from the catalogue of Omnidea-RTG [9], where the values of concentrated
losses are indicated. The relevant parameters for pipes and valves are available in Appendix
E.
To compute the pressure losses, the losses of the injectors and cooling jacket are considered
with respect to Pc; in particular: dPcool = 15% of Pcand dPinj = 40% of Pc.
Starting from the value of Isand OF computed before, it’s possible to evaluate mprop,mf u
and mox and, consequently, Vprop ,Vf u,Vox that are necessary to set the pressures inside the
tanks and characterize the dimensions of the tanks. After the first approximation is possible
to set a precise length of the pipes, necessary to calculate the correct values of distributed
losses. All the procedure is repeated in order to obtain the correct sizing of the three tanks.
In the sections below, it’s possible to see how the feeding line changes with the two different
propellants. The procedure followed is the same in both cases.
6.1 Toxic propellant
The main values found for the pressurizing gas are reported in the Tab 6.1
Size Mass [Kg]Volume [m3]Pressure [bar]
S1.444 0.064 13.79
M1.447 0.064 13.83
L1.459 0.064 13.95
Table 6.1: Main Values for Pressurizing Gas for T-kick
Starting from this data, the spherical shape for the Helium tank is selected due to the
higher strength with respect to the cylindrical one; in addition to this, in this case, the volume
of gas is not very large, so the spherical shape of the tank will not take much space. The
material chosen is aluminium because it’s lightweight and affordable. The size of the tank is
the following:
Size Radius [m]Thickness [mm]Mass [kg]
S0.249 0.341 0.750
M0.249 0.342 0.752
L0.249 0.345 0.759
Table 6.2: Size of Helium tank for T-kick
In the tables below, it’s possible to see the values that characterize the fuel and oxidizer:
Size Mass [Kg]Volume [m3]Pressure [bar]
S180.126 0.179 13.05
M180.126 0.179 13.09
L180.126 0.179 13.19
Table 6.3: Main Values for Fuel for T-kick
16
Size Mass [Kg]Volume [m3]Pressure [bar]
S162.113 0.112 13.06
M162.113 0.112 13.09
L162.113 0.112 13.19
Table 6.4: Main Values for oxidizer for T-kick
For the reasons presented before, the choices made for the tanks of fuel and oxidizer are
the same as the helium one: so, spherical shape with aluminium as material. Below, the
dimensions of the tanks are shown:
Size Radius [m]Thickness [mm]Mass [kg]
S0.345 0.454 1.965
M0.345 0.455 1.969
L0.345 0.458 1.985
Table 6.5: Size of Fuel tank for T-kick
Size Radius [m]Thickness [mm]Mass [kg]
S0.299 0.388 1.225
M0.299 0.388 1.226
L0.299 0.389 1.231
Table 6.6: Size of Oxidizer tank for T-kick
6.2 Green propellant
The procedure followed is the same as before, but the different type of fuel and oxidizer requires
to re-valuate the decisions taken in the previous section. In Tab 6.7 it’s possible to see the
main properties of the pressurizing gas.
Size Mass [Kg]Volume [m3]Pressure [bar]
S1.391 0.062 13.81
M1.397 0.062 13.86
L1.418 0.062 14.08
Table 6.7: Main Values for Pressurizing Gas for G-kick
The values of volume and pressure of Helium in G-kick are very similar to the values in
T-kick, so the decisions made for the shape and the material of the tank are the same as
before (spherical shape and aluminium). In Tab 6.8, the dimensions of the tank are given:
Size Radius [m]Thickness [mm]Mass [kg]
S0.246 0.338 0.723
M0.246 0.339 0.726
L0.246 0.344 0.737
Table 6.8: Size of Helium tank for G-kick
17
The last topic of this section is to see how the values of fuel and oxidizer change and,
consequently, if the shape and material of the tanks have to be changed or can be kept as in
T-kick. Look at the Tab 6.9 and Tab 6.10:
Size Mass [Kg]Volume [m3]Pressure [bar]
S57.514 0.070 13.05
M57.514 0.070 13.05
L57.514 0.070 13.06
Table 6.9: Main Values of Fuel for G-kick
Size Mass [Kg]Volume [m3]Pressure [bar]
S301.95 0.210 13.07
M301.95 0.210 13.12
L301.95 0.210 13.34
Table 6.10: Main Values of oxidizer for G-kick
Looking at the results, it’s evident that the volumes and the pressures of fuel and oxidizer
are comparable with previous ones, so the spherical shape is kept also in G-kick. About
the material, the H2O2is not compatible with titanium, so, for the oxidizer tank, the use of
aluminium is necessary; the same material is selected also for the fuel tank.
Size Radius [m]Thickness [mm]Mass [kg]
S0.256 0.331 0.768
M0.256 0.332 0.768
L0.256 0.332 0.768
Table 6.11: Size of Fuel tank for G-kick
Size Radius [m]Thickness [mm]Mass [kg]
S0.368 0.479 2.304
M0.368 0.481 2.313
L0.368 0.489 2.352
Table 6.12: Size of Oxidizer tank for G-kick
6.3 Trade off comparison
The same feeding system and tank design has been adopted for both toxic and green nominal
solution. Despite that, the different propellants have induced a difference in the sizing, due to
their different physical properties.
Considering the pressurizing gas tank is it possible to observe different mass and geomet-
rical properties between the nominal solutions, due to a little difference in the pressure. In
particular, the pressurizing gas tank for the T-Kick M is bigger and heavier than the green
nominal solution’s one.
18
On the other hand, looking at the tanks for fuel and oxidizer, a higher difference can be
noticed. The difference in the physical properties between the two propellants couple produce
a fuel tank smaller and lighter for the G-Kick M with respect to the T-Kick M meanwhile
the oxidizer tank appears bigger and heavier.
7. Cooling Design
7.1 Thermal analysis
To approximate the behaviour of the heat flux along the engine, different models were adopted.
The Dittus-Boelter correlation (eq:F.5 ) is used to compute the heat transfer coefficient in
the combustion chamber and in the throat section assuming constant properties in these por-
tions.
Proceeding along the nozzle, the Bartz model (eq:F.6) is then adopted beyond the throat where
the properties of the fluid (T, cp,µ,ρ, K, M) are obtained from the CEA code “cutting” the
divergent part at different expansion ratios. The parabolic trait of the Rao nozzle is approx-
imated as a conical trunk and divided into smaller trunks of constant height, corresponding
to the section considered in the CEA code.
By using F.1 to find the recovery factor, the adiabatic wall temperature is computed F.2.
The temperature T0is the imposed wall temperature to grant the material integrity.
Due to the shortness of the convergent part of the nozzle, a linear behaviour is assumed
between the specific heat flux in the combustion chamber and the value in the throat while in
the divergent is instead applied a fitting.
Figure 7.1: Specific heat flux trend along the CC and the nozzle (red)
The heat flux was finally computed by multiplying the specific value for the corresponding
exchange surfaces. This analysis can be considered as a preliminary and simple evaluation of
19
the heat flux behaviour along the engine, in fact in the chamber part where is applied Dittus-
Boelter relation, the correlation range on D/L is not always satisfied (while the requirements
on Reynolds’ and Prandtl’s number were verified).
Size Qcc [W] Qconv [W] Qdiv [W] Qtot [W]
S1.268 ·1041.069 ·1032.613 ·1031.632 ·104
M1.671 ·1041.998 ·1034.895 ·1032.360 ·104
L2.222 ·1043.723 ·1033.823 ·1032.977 ·104
Table 7.1: Heat transfer for T-kick
Size Qcc [W] Qconv [W] Qdiv [W] Qtot [W]
S2.344 ·1049.717 ·1022.290 ·1032.670 ·104
M3.071 ·1041.806 ·1034.270 ·1033.678 ·104
L4.048 ·1043.377 ·1037.970 ·1033.183 ·104
Table 7.2: Heat transfer for T-kick
The material chosen for the combustion chamber and nozzle is C-103, a Niobium alloy,
typically used for this kind of application in the last 20 years [31][33][37]. Furthermore, to
avoid degradation of the alloy inside the rocket engine must be applied a layer of R512E, a
silicide anticorrosive coating, able to withstand high temperatures. The C-103 main feature
are reported in table9.1:
M ST [K]Tf us[K]ρ[kg/m3]Tcor r[K]
1673.15 2623.15 8850 773.15
Table 7.3: C-103 main features
7.2 Cooling strategy
For the survivability of the engine, it is crucial to design a cooling system that dissipates the
generated heat. Approximating for simplicity the nozzle as conical the heat flux in the three
sections can be computed.
An initial analysis has been pursued on the regenerative method. The increase in the
temperature of the fuel used as cooling liquid in the combustion chamber overcomes the
maximum admittable values. Instead, the increase along the divergent or convergent part of
the nozzle is small enough to make possible the adoption of this strategy. Both hydrazine in
the toxic case and RP1 in the green case are introduced at 298.15K, while their maximum
admittable values in order to avoid boiling are respectively 387.15K and 450K.
Size Tcc [K] Tconv [K] Tdiv [K]
S343.88 28.65 64.13
M227.81 26.81 59.97
L125.03 27.22 23.49
Table 7.4: Cooling liquid temperature increase for T-Kick
20
Size Tcc [K] Tconv [K] Tdiv [K]
S2265.1 93.9 221.3
M1483.7 87.2 206.3
L978.0 81.6 192.5
Table 7.5: Cooling liquid temperature increase for G-Kick
Reassuming, the regenerative cooling strategy is not feasible for the following reasons:
The C-103 will overcome its MST;
The hydrazine will start to damage the cooling channel’s wall
The hydrazine’s temperature variation in to much higher than admissible
Anyway, the problem of dissipating the heat in the other portions remained, and so, using
F.4 the heat flux that could be dissipated in a radiative way in the different portions was
evaluated, but the value was not sufficient with respect to the needed one, in particular in
the combustion chamber, even assuming an external temperature close to 0K. In most cases,
instead, the divergent part could be cooled in this way.
Size Qcc [W] Qconv [W] Qdiv [W] Qtot [W]
S9.023 ·1032.825 ·1021.934 ·1042.865 ·104
M1.279 ·1045.660 ·1023.868 ·1045.204 ·104
L1.824 ·1041.131 ·1033.235 ·1045.172 ·104
Table 7.6: Radiative dissipated heat for T-kick
Size Qcc [W] Qconv [W] Qdiv [W] Qtot [W]
S1.841 ·1042.748 ·1021.866 ·1043.734 ·104
M2.585 ·1045.468 ·1023.733 ·1046.373 ·104
L3.652 ·1041.096 ·1037.469 ·1041.123 ·105
Table 7.7: Radiative dissipated heat for G-kick
Looking at the literature and on the existing rocket engine with C103, a film cooling strat-
egy in addition to the radiative is used to dissipate the heat and guarantee the survivability
of the engine.
The film cooling strategy decreases the performances of the rocket engine, by decreasing the
O/F ratio. To apply this cooling strategy is necessary to change the geometrical configuration
of the injection plate, adding apposite injectors for that scope. It’s necessary to change the
model in the order to compute the performance parameters of the engine with this cooling
strategy and do experimental tests.
Finally, an alternative cooling strategy can be considered using the same alloy (C-103) for
the wall of the combustion chamber and nozzle, but applying a thermal barrier coating. The
material chosen is zirconium-dioxide. (Service temperature is between 1250K÷2200Kand
Kis about 1.7÷2.5).
In order to maintain the thickness of the coating around 500µm, even considering its very
low thermal conductivity, and in order to remain within the admissible temperature limit of
21
the C103 alloy, the temperature of the gas side to be kept to improve the adoption of the
previous exposed methods, in particular in the combustion chamber, is 1900K. This value also
grants, for the fixed thickness, the interface with the Niobium alloy to stay below its MST.
8. Engine Upscaling and Downscaling
After the design of the nominal solutions for the two different propellants (toxic and green), an
engine analysis of the downscaling and upscaling is conducted. The downscaling is carried out
by halving the nominal thrust, while the upscaling doubling it. The only parameter changed
during this study is T, to obtain a set of three engines for each of the two propellant solutions,
able to ensure the same performance parameters.
For what concerns the scaling outputs for the nozzle’s performance parameters and design, it
is possible to observe a change in ˙mlinear dependent to the thrust, such as in Ac,Atand Ae.
On the other hand, depending on the section diameter, the length of the nozzle’s convergent
and divergent wall increases from the downscaled motor to the upscaled one with a trend
depending on the square root of the sections’ areas, and so linearly dependent on the square
root of the thrust.
Subsequently, also the total length of the nozzle presents a linear trend with respect to the
square root of the thrust.
On the other hand, considering the combustion chamber, it is just known that Acvaries
linearly with the thrust. Furthermore, the linear variation of the throat section area, with re-
spect to the thrust, drives a variation in the combustion chamber volume with the same trend.
Looking at the injection plate the downscaling and upscaling process implies a variation in the
number of holes to guarantee the correct propellant mass flow rate on the combustion cham-
ber and nozzle. The change in the holes’ number drives, apart from a different geometrical
configuration of the injectors, also to a different mass flow rate of fuel and oxidizer through
each injector. The variation of the geometrical properties of the injectors implies finally a
variation in the point of impingement with respect to the plate surface. The only parameter
that remains constant is the injection velocity.
About the feeding line, the scaling of the engine doesn’t affect the geometry too much. In
T-kick, the radius of the three tanks doesn’t change at all; there is a small increase in the
mass value due to the increase in the thickness. The thickness is related to the pressure that
grows a little with the growth of the T. In G-kick the behaviour of the results is the same as
in the case before.
9. Additive Manufacturing
The selection of the material is carried on by the requirements of resistance to the maximum
temperature, printability and compatibility with the propellant used, both the toxic and green
one.
Regarding the printability properties, for this design the manufacturing technique chosen
is L-PBF (Laser Powder Bed Fusion), known also as SLM (Selective Laser Melting), due to
22
its high level of accuracy even with high-temperature resistant alloys [36].
Another motivation for this choice is that structural tests have shown good results [35].
Laser diameter [µm]Accuracy[µm]Bed[mm]
100 ±20/50 400x400x400
Table 9.1: Additive manufacturing features of EOS M 400 Series
Another advantage of this technique is that, due to its precision, don’t require additional
tooling to smooth the combustion chamber or the nozzle or drill the injectors. Nevertheless,
the injectors are designed with a minimum diameter of 0.0004 m, imposing a tolerance much
higher than the capability of L-PBF. Also is recommended to manufacture the injection plate
in two separate parts: the one with the injectors, will be printed in a mono-block with the
combustion chamber, while the other with the distribution system of fuel and oxidizer will be
printed separately, in case additional tooling for the injector is needed.
To guarantee better isotropy of the material, each layer will be rotated of an angle depending
on the structural requirements. In addition, to relieve the stress generated during the manu-
facturing, a heat treatment, at about 1000C, is recommended. [35]
Knowing that the niobium alloy is subjected to oxidation, at temperatures higher than 500C,
a chemical protection coating is needed. This problem can be overcome by the insertion of a
coating surface such as silicide coats (R-512E) in the form of a slurry layer that will solidify.
[40][41]
In this case, the machine will not be able to accommodate all the engine printed in one
piece. So, it’s necessary to manufacture the combustion chamber, till a short after the throat
to avoid structural failure, and part of the divergent nozzle at two different times. Successively
they are welded together.
10. Conclusion
The aim of this work was to develop a preliminary design of a set of two kick stage rocket
motors, one using toxic propellant and the other a green one, downscaling and upscaling them
with respect to the thrust. The results obtained need to be supported and confirmed by tests
on the final motor to assure the real capability of guaranteeing the theoretical performance; in
particular, due to the simplicity of the model adopted in the thermal analysis of the cooling
strategy, further tests are needed in order to validate the results.
Itot[N·s]tb[h]
S M L
T-kick 1.0285 ·1062.857 1.428 0.714
G-kick 1.0451 ·1062.903 1.451 0.726
Table 10.1: final comparison between the T-kick and G-kick
In the Tab 10.1, the values for Itot and tbfor T-kick e G-kick are shown. It’s possible to
see that for G-kick both values reported are higher.
23
Looking at the results, the toxic option seems to be the most convenient one because, for a
little smaller values of Itot and tb, T-kick is smaller than G-kick so more affordable from the
point of view of the dimensions; in addition to this H2O2, used in the green stage, is not the
best option for its high level of corrosivity, much higher than the hydrazine used in the toxic
case.
To choose the best scaling, it’s necessary to take into consideration the entity and the number
of manoeuvres that characterize the mission: for missions with a small number of manoeuvres,
but characterized by a big entity the up-scaling is the option recommended for the less value
of tband the higher thrust produced; on the other hand, in case of missions with many small
manoeuvres a down-scaling is the best solution, since the higher tbguarantees a higher number
of smaller thrusts. The nominal case, finally, is the one with greater versatility, so is suitable
for missions where the entity and the duration of the manoeuvres is variable.
In order to make a decision, it’s recommended to take into consideration other points of view
as cost analysis or material durability.
24
1. Appendix A
CEA code
A.1 Toxic propellant
Figure A.1: CEA code in toxic propellant case
I
B.2 Green propellant
Figure A.2: CEA code in green propellant case
II
2. Appendix B
Nozzle Design
A.1 Isoentropic and performance parameters equations
1
ϵ=γ+ 1
21
γ1Pe
P01
γv
u
u
t
γ+ 1
γ1"1Pe
P0γ1
γ#(B.1)
cF=s2γ2
γ12
γ+ 1γ+1
γ1s1Pe
Pcγ1
γ
+PePa
Pc
ϵ(B.2)
ve=v
u
u
t
2γ
γ1RTc"1Pe
Pcγ1
γ#(B.3)
˙m=hTPe
PaAei
ve
(B.4)
Is=T
˙m·g0
(B.5)
ϵ=1
Mes2
γ+ 1 1 + γ1
2M2γ+1
γ1
(B.6)
III
Figure B.1: RAO’s parabolic approximation for bell nozzle design
IV
3. Appendix C
CC Design
Figure C.1: The characteristic length for different propellants
V
4. Appendix D
Injectors
Figure D.1: Discharge Coefficient
VI
5. Appendix E
Feeding line design
A.1 Pipes
The pipes chosen are made of AISI 316 stainless steel with nominal diameter of 1/4” produced
by Swagelok [11]; the main properties are shown in table E.1.
Tube OD [mm]Tube Wall
[mm]
Working Pres-
sure [bar]
Tensile
strength
[M P a]
Roughness
[µm]
6.35 0.889 352.64 580 30
Table E.1: Values of 1/4” stainless steel pipe
B.2 Valves
The catalog of Omnidea-RTG [9] provides a collection of valves for the feeding line. All the
valves are compatible with a large variety of propellants and with the 1/4” pipes used in the
rest of the feed system.
In the tables below the properties of the valves are shown.
Gas Pressure Regulator
MEOP [bar]Max Flow
Rate [g/s]
Pressure Drop
[bar]
Pressure Port
350 1,8 - 1/4” welding tube
Table E.2: Values of Gas Pressure Regulator
Check Valve
MEOP [bar]Max Flow
Rate [g/s]
Pressure Drop
[bar]
Pressure Port
35 2 <0.5 1/4” welding tube
Table E.3: Values of Check Valve
VII
Latch Valve
MEOP [bar]Max Flow
Rate [g/s]
Pressure Drop
[bar]
Pressure Port
0-350 30 <0,1 1/4” welding tube
Table E.4: Values of Latch Valve
6. Appendix F
Cooling design
Rec =1 + P r 1
3y1
2M2
1 + y1
2M2; (F.1)
Taw =RecT0(F.2)
q=hg(Taw Twg ) ; (F.3)
Q=AσeT 4
wg ; (F.4)
NuDh = 0.023Re0.8
DhP r 0.4
0.6P r 160
ReDh >10000
L
D>10
(F.5)
hg=0.026
D0.2
iµ0.2cp
P r0.6ns (pc)ns
¯c0.8Dt
¯
R0.1At
A0.9σ
σ=1
h1
2
Twg
(Tc)ns (1+ γ1
2M2)+1
2i0.68[1+ γ1
2M2]0.12
(F.6)
VIII
Bibliography
[1] https://www.nasa.gov/smallsat-institute/sst-soa/in-space-propulsion nasa.org
[2] Stefania Carlotti and Filippo Maggi. Evaluating new liquid storable bipropellants: ”Safety
and performance assessments. Aerospace, 9(10):561, 2022”
[3] Adam Okninski, Pawel Surmacz, Bartosz Bartkowiak, Tobiasz Mayer, Kamil Sobczak,
Michal Pakosz,Damian Kaniewski , Jan Matyszewski, Grzegorz Rarata and Piotr Wolanski.
”Development of Green Storable Hybrid Rocket Propulsion Technology Using 98% Hydrogen
Peroxide as Oxidizer”, 2019
[4] arianegroup, chemical bi-propellant thruster family
[5] Livia Ordonez Vallesa,b, Arturs Jasjukevicsc, Marco Wolfc, Lily Blondel Caneparie, Uwe
Apela, Martin Tajmarb, Angelo Pasini. ”LunaNova kick stage: an overview of the system
propulsion trade-offs”, 2022
[6] Bondugula Mary Sharon Rose, Gorakula Srilochan. ”Hydrogen peroxide based green pro-
pellants for future space propulsion applications”, 2021
[7] Lily Blondel-Canepari, Livia Ordonez-Valles, Arturs Jasjukevics, Marco Wolf, Stephane
Dussy, Uwe Apel, Martin Tajmar, Angelo Pasini. ”Roadmap Towards a Greener Kick-
Stage Propulsion System”, 2022
[8] Lily Blondel-Canepari, Livia Ordonez-Valles, Arturs Jasjukevics, Marco Wolf, Stephane
Dussy, Uwe Apel, Martin Tajmar, Angelo Pasini. ”Roadmap Towards a Greener Kick-
Stage Propulsion System”, 2022
[9] Omnidea-RTG, ”Space Propulsion Components, Product Catalogue”, February 2016
[10] George P.Sutton,Oscar Biblarz, ”Rocket Propulsion Elements”,2017
[11] Swagelock, ”Stainless Steel Seamless Tubing and Tube Support Systems”,2021
[12] ”https://www.space-propulsion.com/spacecraft-propulsion/bipropellant-thrusters/200n-
bipropellant-thrusters.html”
[13] Prithvi D. Awasthi, Priyanka Agrawal, Ravi Sankar Haridas, Rajiv S. Mishra, Michael
T. Stawovy, Scott Ohm, Aidin Imandoust. ”Mechanical properties and microstructural
characteristics of additively manufactured C103 niobium alloy”, 2022
[14] https://rocketcea.readthedocs.io/en/latest/finite area comb.html
[15] https://www.alphaprecisionpm.com/blog/what-is-metal-additive-manufacturing
[16] Omar R. Mireles, Omar Rodriguez, Youping Gao, Noah Philips. ”Additive Manufacture
of Refractory Alloy C103 for Propulsion Applications”,- Albany, OR, 97321, USA, 2020
[17] D. K. Huzel, D. H. Huang.”Modern Engineering for Design of Liquid-Propellant Rocket
Engines”,- AIAA 1992
[18] Dirk Herzog, Vanessa Seyda, Eric Wycisk, Claus Emmelmann. ”Additive manufacturing
of metals”,2016
IX
[19] V. G. Varanasi, T.M. Besmann, J.L. Lothian, W. Xu, T.L. Starr ”Chemically vapor
deposited yttria-stabilized zirconia (YSZ) for thermal and enviromental barrier coating”
[20] SpaceFlight. Sherpa Payload User’s Guide
[21] Alberto Sarritzu, Lily Blondel-Canepari, Riccardo Gelain. ”Trade-off study of green tech-
nologies for upper stage applications Conference Paper”,2022
[22] Lily Blondel-Canepari, Livia Ordonez Valles, Martin Tajmar. ”Roadmap Towards a
Greener Kick-Stage Propulsion System”,2022
[23] Rocket Lab. ”Launch:Payload User’s Guide”, August, 2020
[24] Dierer K. Huzel and David H. Huang, Rockedyne Division, North Amercican Aviation.
Inc. id 19710019929, ”Design of liquid propellant engines”
[25] A. J. Pavli. id 19800004908,”Design and evaluation of high prformace rocket engive in-
jectors for use with hydrocarbon fuels”
[26] N. Riaud, B. Boust and M.Bellenoue,Atomization and combustion of a single unlike-triplet
spray of storable bipropellants: hydrogen perxide with ethanol or alkanes”
[27] Cl´ement Indiana, Bastien Boust, Nobuyuki Azuma. Combustion of sprays from triplet
injector with green propellants: ethyl alcohol and hydrogen peroxide. 7TH EUROPEAN
CONFERENCE FOR AERONAUTICS AND SPACE SCIENCES (EUCASS), Jul 2017,
Milan, Italy. ffhal-01625647
[28] National Aeronautics and Space Administartion, ”Liquid rocket engine injectors”, id
19760023196
[29] Gang Zheng, Wansheng Nie, Songjiang Feng, Gaoyang Wu, ”Numerical Simulation of the
Atomization Process of a Like-doublet Impinging Rocket Injector”
[30] Anlong YANG , Bin LI, Shangrong YANG, Yunfei XU, Longfei LI, ”Periodic atomization
characteristics of an impinging jet injector element modulated by Klystron effect”
[31] John W Dankanich, Youping Gao, Steven S Shaw, Artra C Thompson, ”Additive Manu-
facturing of Refractory Metal Nb Alloy C103 for Propulsion Applications”
[32] Hankwitz, J.P.; Ledford, C.; Rock, C.; O’Dell, S.; Horn, T.J. Electron
Beam Melting of Niobium Alloys from Blended Powders. Materials 2021, 14, 5536.
https://doi.org/10.3390/ma14195536
[33] Omar R. Mireles, Omar Rodriguez, Youping Gao, Noah Philips, ”Additive Manufacture
of Refractory Alloy C103 for Propulsion Applications”
[34] Thato Sharon Tshephe, Samuel Olukayode Akinwamide, Eugene Olevsky, Peter Apata
Olubambi, ”Additive manufacturing of titanium-based alloys- A review of methods, prop-
erties, challenges, and prospects”
[35] Prithvi D. Awasthi, Priyanka Agrawal, Ravi Sankar Haridas, Rajiv S. Mishra, Michael
T. Stawovy, Scott Ohm, Aidin Imandoust, ”Mechanical properties and microstructural
characteristics of additively manufactured C103 niobium alloy”
[36] Luo Zhang, Shasha Zhang, Haihong Zhu, Zhiheng Hu, Guoqing Wang, Xiaoyan Zeng,
”Horizontal dimensional accuracy prediction of selective laser melting”
X
[37] John Hebda, ”NIOBIUM ALLOYS AND HIGH TEMPERATURE APPLICATIONS”
[38] Brian Reed, James Biaglow and Steven Schneider, NASA Lewis Research Center”, ”AD-
VANCED MATERIALS FOR RADIATION-COOLED ROCKETS”
[39] John Hebda, ”NIOBIUM ALLOYS AND HIGH TEMPERATURE APPLICATIONS”
[40] SHAIKH Asad Ali Dilawary, MUHAMMAD Khalid, AMJAD Ali, and HAMID
Zaigham.”Effect of Low Temperature Heat Treatment for R512E Coated C-103 Nb Alloy”
[41] Mark D. Novak, Carlos G. Levi, University of California, Santa Barbara, Materials De-
partment.”OXIDATION AND VOLATILIZATION OF SILICIDE COATINGS FOR RE-
FRACTORY NIOBIUM ALLOYS”
[42] https://www.azom.com/properties.aspx?ArticleID=133
[43] https://www.launcherspace.com/orbiter
[44] https://spaceflight.com/sherpa/
[45] https://www.skyrora.com/space-tug/
[46] https://www.rocketlabusa.com/space-systems/photon/
XI
ResearchGate has not been able to resolve any citations for this publication.
Conference Paper
Full-text available
The fast-paced growth of the space sector brings in new challenges especially with upcoming complex missions combining multi-orbit deliveries and/or on-orbit servicing such as Active Debris Removal (ADR). Europe has taken up the challenges and is working on extending its launchers portfolio and capabilities. In this framework, a new add-on, the kick stage, confers strategic advantages to the launcher in expanding its missions' range. While many kick stages are currently developed, or already in use worldwide, this paper pays a particular attention to the new ASTRIS kick stage developed and optimized for A6 and its next kick stage generation already under conceptual study, LunaNova, at ArianeGroup Bremen for A6 Evolution. The project takes place under the ESA Future Launchers Preparatory Programme (FLPP) and is already implementing new technologies, namely innovative pressurization system and green propellants which are of special interest here. The paper starts by introducing the kick stage capabilities, especially the LunaNova ones, to then focus on the cost-oriented trade-off performed to select the fuel to use in combination with 98%-HTP to power the LunaNova vehicle. The paper then concludes by discussing the system impacts of implementing green propellants within the operational kick stage life cycle and its possible enhancement (namely the implementation of an e-pump).
Article
Full-text available
Conventional storable bipropellants make use of hydrazine and its derivatives as fuels and nitrogen tetroxide as an oxidizer. In recent years, the toxicity character of these chemicals pushed the propulsion community towards “green” alternatives. Several candidates have been proposed among existing and newly developed chemicals, highlighting the need for a common and robust selection methodology. This paper aims at reviewing the most important selection criteria in the field of toxicity and discusses how to objectively define a green propellant, considering both the health and environmental hazards caused by the chemicals. Additionally, consistent figures of merit in the field of safety and handling operations and performance are proposed. In particular, operating temperatures, flammability and stability issues are discussed in the framework of physical hazards and storage requirements, while vacuum impulses, adiabatic flame temperature and sooting occurrence of the investigated couples are compared to the UDMH/NTO benchmark case. Hydrogen peroxide and nitrous oxide, and light hydrocarbons, alcohols and kerosene are selected from the open literature as promising green oxidizers and fuels, respectively. The identified methodology highlights merits and limitations of each chemical, as well as the fact that the identification of a universally best suited green couple is quite impractical. On the contrary, the characteristics of each propellant lead to a scenario of several “sub-optimal” couples, each of them opportunely fitting into a specific mission class.
Conference Paper
Full-text available
As an emerging trend, Green Propulsion has been exponentially growing over the last decades in the space sector. This paper assesses different technologies in a trade-off study weighting their applicability to a specific class of upper stage systems, currently developed by many companies and often referred to as kick-stages or orbital stages. In a generic two-stage-to-orbit scenario, many launchers require a system able to go the ‘extra-mile’ to deliver one or multiple payloads on orbit(s). That is where the kick stage comes into playing a crucial role. The trade-off study reported here is based on a well-known decision-making tool, the Analytical Hierarchy Process. The main results are a technologies evaluation framework, strongly requirements-oriented, that allows to select the most promising candidates for various scenarios, and a preliminary technology selection. The screening is divided into liquid low-thrust class engines, usually employed for attitude and reaction control thrusters; and liquid high-thrust engines such as hypergolic bi-propellants combinations, commonly used for apogee manoeuvres. Finally, the evaluation framework is tested on Hybrid thrusters to examine its flexibility in a dedicated parallel trade-off.
Article
Full-text available
Niobium-based tungsten alloys are desirable for high-temperature structural applications yet are restricted in practice by limited room-temperature ductility and fabricability. Powder bed fusion additive manufacturing is one technology that could be leveraged to process alloys with limited ductility, without the need for pre-alloying. A custom electron beam powder bed fusion machine was used to demonstrate the processability of blended Nb-1Zr, Nb-10W-1Zr-0.1C, and Nb-20W-1Zr-0.1C powders, with resulting solid optical densities of 99+%. Ultimately, post-processing heat treatments were required to increase tungsten diffusion in niobium, as well as to attain satisfactory mechanical properties.
Article
Full-text available
This paper presents the development of indigenous hybrid rocket technology, using 98% hydrogen peroxide as an oxidizer. Consecutive steps are presented, which started with interest in hydrogen peroxide and the development of technology to obtain High Test Peroxide, finally allowing concentrations of up to 99.99% to be obtained in-house. Hydrogen peroxide of 98% concentration (mass-wise) was selected as the workhorse for further space propulsion and space transportation developments. Over the course nearly 10 years of the technology’s evolution, the Lukasiewicz Research Network—Institute of Aviation completed hundreds of subscale hybrid rocket motor and component tests. In 2017, the Institute presented the first vehicle in the world to have demonstrated in-flight utilization for 98% hydrogen peroxide. This was achieved by the ILR-33 AMBER suborbital rocket, which utilizes a hybrid rocket propulsion as the main stage. Since then, three successful consecutive flights of the vehicle have been performed, and flights to the Von Karman Line are planned. The hybrid rocket technology developments are described. Advances in hybrid fuel technology are shown, including the testing of fuel grains. Theoretical studies and sizing of hybrid propulsion systems for spacecraft, sounding rockets and small launch vehicles have been performed, and planned further developments are discussed.
Article
Full-text available
An experimental study on the Klystron effect of periodic injection modulated by pressure drop fluctuations on subsequent atomization is conducted. Time-resolved atomization backlit images and atomization Mie scatter images are captured by using the high speed camera. It is found that periodicity of forced atomization relies on pressure drop fluctuation amplitude and phase differences between atomization and pressure drop fluctuations relate to fluctuation frequencies. This feature of periodic atomization induced by Klystron effect corresponds to periodicities and high amplitudes of pressure fluctuations in unstable combustion chambers and chaos and low amplitudes of pressure fluctuations in stable combustions chambers. Drastically periodic varying of gross surface area of droplets with time was shown in Mie scatter images. The importance of periodic impinging jet atomization modulated by pressure drop fluctuations for acoustic liquid propellant combustion instabilities is illustrated.
Conference Paper
C103 is niobium alloy used in high temperature operating environments. Traditional manufacture methods suffer from feedstock constraints, difficult to machine, high buy-to-fly ratios, and high costs resulting in a limited number of suppliers. Additive manufacture (AM) offers advantages in production of complex parts, improved properties, reproducibility, with significant material cost and schedule savings. The objectives of this project was to investigate the feasibility to AM C103, develop powder feedstock, optimize process parameters, establish design criteria, investigate post-process heat treatments, and determine material properties. AM C103 proved feasible, increased design flexibility, improved mechanical properties compared to wrought, and resulted in an order of magnitude cost reduction.
Conference Paper
The present study focuses on the atomization and combustion of sprays generated by an unlike triplet injector, using hydrogen peroxide as oxidizer in association with ethanol or alkanes as fuels. Two injectors are tailored specifically for the fuels for a total flowrate of 10 g/s. The combustion chamber allows shadowgraphy and chemiluminescence visualizations. A characterization of the spray is performed in both reactive and inert conditions using high-magnification shadowgraphy. The performances are compared at steady-state in terms of characteristic velocity efficiency within a range of equivalence ratio 0.5-2.0 and pressure 3-6 bar.
Article
A theoretical model has been proposed to predict the horizontal dimensional accuracy of selective laser melting (SLM) in this paper. It is found that the horizontal dimensional deviation of SLM consists of two parts. The first part is related to the mode of track filling and the track width. The effect of heat accumulation on track width is also taken into account in this model. The second part is the solidification shrinkage which is dominated by the temperature history of the tracks of a layer when the material and dimension size are fixed. Then, the SLMed Ti6Al4V parts fabricated to verify this theoretical model has been performed in this paper too. The results show that the predicted and experimental results has a good correspondence. At last, less than 20μm dimension deviation of SLMed thin-wall samples was achieved by pre-compensation using this theoretical model.