Applied Energy 220 (2018) 921–933
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
Cold gas propulsion microthruster for feed gas utilization in micro satellites
a,⁎
b
a
R. Ranjan , K. Karthikeyan , F. Riaz , S.K. Chou
a
b
T
a
Department of Mechanical Engineering, Nus, 5 Engineering Drive, 117608 Singapore, Singapore
A*STAR, c/o SIMTech,2 Fusionopilis Way, #08-04, 138634 Singapore, Singapore
H I GH L IG H T S
the pressure feed gas to extend the life of microsatellites.
• Utilise
gas propulsion system development for liquid propelled system.
• Cold
nozzle performance study of liquid fuelled chip using compressed gas.
• Micro
vacuum and sea level condition experimental testing.
• Simulated
Numerical
model validation with vacuum and sea level experimental results.
•
A R T I C LE I N FO
A B S T R A C T
Keywords:
Microthruster
Cold gas propulsion
CubeSats
Attitude control
Feed gas utilization
Micro spacecraft, which have gained huge popularity in the last decade, are termed as “CubeSats”, a well-known
class of small satellites. The fast growing functionality and popularity of CubeSats have helped researchers push
technology demonstration towards efficient performance and reliability needed for commercial and governmental applications. Keeping in mind the increasing space debris, dependence of satellite life on fuel, and the use
of fossil fuels as propellants, recent efforts are being made to develop a cold gas propellant-based (CGP) micro
propulsion system. The CGP system has various merits, namely, non-toxicity, easy to use, and low leakage
concerns over other propulsion systems. Liquid propellant-based propulsion requires a liquid feed system, which
uses pressurized gas (such as helium, argon and nitrogen) to pressure-feed liquid to the combustion or vaporization chamber so as to produce thrust. But once the liquid propellant is depleted, the pressurized gas is
unusable while the system runs out of fuel. Thus, the proposed CGP system being studied, apart from being used
as a normal cold gas propulsion system, also offers the advantage of being used as a propulsion system for a
liquid fueled system, in the event the liquid fuel runs out. The present work reports on cold gas micro thruster
development, utilization of feed gas in a liquid fueled thruster, and the experimental study on the CGP system in
simulated vacuum conditions and under a range of pressure conditions. Pressure in the pressure feed gas system
for a 1–50 kg category of satellites varies from 4 to 8 bar depending on the mission requirement. The pressure
reduces as the liquid propellant gets exhausted. The experimental results are used to validate a computational
fluid dynamics model of the system. Thrust values are obtained between the micro to milli-Newton range so as to
fulfil the requirements of attitude and station keeping for CubeSats in the 1–50 kg dry mass range. Under vacuum
conditions, we obtained thrust values of 0.8 mN at 1 bar feed pressure to 2.24 mN at 4 bar feed pressure. These
thrust values are nearly twice those achieved for sea level tests for the corresponding feed pressure. Furthermore,
the parameters such as Mach number, velocity vector, pressure, temperature, specific impulse, and nozzle efficiency are studied and reported for atmospheric and vacuum conditions.
1. Introduction
In recent years, thousands of microspacecraft have been launched
into space for remote sensing, earth observation, technology verification and telecommunication. These microspacecraft, which gained huge
popularity in the last decade, are known as “CubeSats”, a well-known
⁎
Corresponding author.
E-mail address: raviranjan@u.nus.edu (R. Ranjan).
https://doi.org/10.1016/j.apenergy.2018.03.040
Received 31 October 2017; Received in revised form 8 March 2018; Accepted 18 March 2018
Available online 21 March 2018
0306-2619/ © 2018 Elsevier Ltd. All rights reserved.
class of small satellites. As the name suggests, this class of micro satellite looks like a cube with a standard unit “U” in terms of size, where
1U represents a CubeSat equivalent of 10 cm × 10 cm × 10 cm in
length, width and height, respectively. The fast growing functionality
and popularity of CubeSats have helped researchers push technology
demonstration towards efficient performance and reliability needed for
Applied Energy 220 (2018) 921–933
R. Ranjan et al.
Nomenclature
Wc
Wt
W
e
Wd
Wi
Lv
T
F
ε
α
ve
Pc
mN
Pe
pC/N
I
I
s
ṁ
Cf
C∗
chamber width (µm)
nozzle throat width (µm)
nozzle exit width (µm)
chamber depth (µm)
inlet diameter (µm)
vaporization chamber length (mm)
temperature (°C)
thrust (mN)
expansion ratio
convergent/divergent angle (°)
exit vapour velocity (m/s)
chamber pressure (bar)
milli-Newton
exit pressure (bar)
picocoulombs per Newton
impulse bit (mN s)
specific impulse (s)
mass flow rate (mg s−1)
thrust correction factor
characteristic velocity
Abbreviations
VLM
LEO
PDMS
CGP
vaporizing liquid microthruster
low earth orbit
polydimethylsiloxane
cold gas propulsion
orientation and precise attitude control. The flow velocity is calculated
for the microthruster using the finite volume method. The system was
miniaturized for a satellite having a mass range in the 1–20 kg class.
Furumo [13] at the Hawaii Space Flight Laboratory (HSFL) developed a
prototype of a CGP system for small satellite station keeping, attitude
control and deorbiting. The system could generate a thrust of 0.1–10 N
and specific impulse of 75 s for Lower Earth Orbit (LEO). The system
was able to deliver a velocity change in the range of 55–75 m/s within
the lower orbit range of 350–900 km. Brownell [14] designed a cold gas
propulsion system to maneuver and stabilize high altitude research
balloons at high altitudes. These balloons are launched to collect data
on weather and chemical composition in the stratosphere.
Commercial software like ANSYS and Autodesk simulation computational fluid dynamics were used to model the system. A convergent
nozzle was used to achieve a thrust of 0.0247 N. Other parameters such
as mass flow rate, inlet pressure and outlet velocities were also analyzed. The finite element analysis for propellant nozzle and tank was
also conducted with the help of Autodesk Inventor [14]. Experience so
far has shown that CGP micro propulsion systems are less expensive
than other propulsion systems making them the preferred candidate for
student micro satellite propulsion projects. Fatehi et al. [15] addressed
the design of CGP systems employing hydrogen, helium, nitrogen,
argon and methane along with eight different material options, namely,
titanium, titanium alloy, magnesium alloy, beryllium alloy, steel,
carbon fiber composites, glass fiber composites and aluminum alloy.
Three optimization methods were used to investigate the optimal
chamber pressure, optimal total mass of the system, radius of the
commercial and governmental applications [1]. Recent surveys report
the impeccable growth of CubeSats during the past decade as shown in
Fig. 1. In 2016, Spaceworks investigated and forecasted the potential
growth of nano/microsatellites in the weight category of 1–50 kg and
found a historical average growth of 39% per year over five years from
2010 to 2015 based on compound annual growth rate [2–3]. Increasing
demand is urging technology development so as to meet market requirements for scalability and flexibility in the new designs. While
looking at the small scale propulsion system market in the near future,
CGP systems demonstrate more promising attributes compared with the
more complex and high temperature based propulsion systems [4] (see
Fig. 2).
Rhee et al. [5] investigated a CGP system, which has proven to be
reliable when tested on larger spacecraft and has the potential to be
miniaturized to meet the requirements of CubeSats. They further reported reliability of the CGP system in delivering thrust in the mN
range. Storck et al. [4] cited various advantages of CGP systems over
other micro propulsion systems, namely, simplicity of design, able to
operate in pulsed or continuous modes, safe to handle, and incurring
less power consumption.
When the hardware complexity is considered, cold gas microthrusters are simpler compared to pulsed plasma thrusters, colloidal
thrusters and field emission electric propulsion thrusters. The main
components of a microthruster include a micro valve, nozzle and storage. The desired thrust is achieved by allowing compressed gas to
discharge through the nozzle. Reichbach [6] investigated size and design requirements such as mass flow, valve dimensions, feed system and
storage tank details. Results show that the response time of the microthruster is higher than the response time required to achieve the
needed thrust value. This leads to the conclusion that the microthruster
is not appropriate for attitude control but sufficient for orbit transfer
and maneuvering. During the course of microthruster development,
various valve configurations have been developed by several groups
including NASA, VACCO industries, CheMS technology, UTIAS, Stanford’s SSD labs, and Uppsala University [5,7–9]. Noci et al. [10] reported the development of a micro propulsion feed module for a CGP
system designed to achieve fine pointing of a scientific satellite. The
micro propulsion subsystem was developed by Noci et al. [10] for environmental disturbances compensation of GAIA spacecraft by controlling the thrust via valve throttling.
On the material front, Lekholm et al. [11] reported the limited
functionality of silicon at high temperature. They developed a ceramic
based cold gas microthruster with an integrated flow sensor allowing
the device to withstand high operating temperature. The sample test
showed that the microthruster could withstand local temperature of
1000 °C. Zirconium dioxide based material is used to demonstrate the
capability of achieving such a high temperature locally within the microthruster. Jerman et al. [12] demonstrated ways to achieve
Fig. 1. Market survey for microsatellite launches history and forecast (1–50 kg) [3].
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R. Ranjan et al.
shown in Table 1.
2.1. Analytical model
The analytical model of the theoretical performance of the microthruster nozzle is based on isentropic, steady state and quasi flow with
the following assumptions:
(i) Propellant is an ideal gas and the flow through the nozzle is
adiabatic.
(ii) Gas flow is frictionless and all boundary layers are neglected.
(iii) No shock wave or discontinuity in the nozzle flow, and the flow of
propellant is assumed to be steady and uniform without vibration.
(iv) The flow leaving the nozzle is axial, and no radial components are
present.
(v) Gas velocity, pressure, temperature, and density are uniform across
any section normal to the nozzle axis.
(vi) Gas used is compressible and there is no chemical reaction, and
chemical equilibrium is established between the gas and thruster
chamber.
Fig. 2. Schematic diagram of microthruster.
propellant tank and principles of structure design. The results point to
nitrogen as the preferred propellant and composites for the CGP system.
Composites are preferred over other materials because they are light
weight. As there is a slim body of published work on CGP systems for
micro satellites, the present study has been initiated with the aim of
filling the gap especially in microthrusters employing liquid fuels.
There is a need to obtain experimental data for a CGP system that can
provide the additional power boost when the liquid fuel is exhausted
and the propulsion has to fall back on the feed gas remaining in a liquid
fueled microsatellite system.
The present study focuses on the design and performance aspects of
the micro nozzle of the microthruster using compressed air as propellant. The set-up also enables the simulation of the real conditions
when feed gas can be used to produce thrust using a vaporizing liquid
microthruster chip when liquid fuel is exhausted. The dual operation of
the microthruster can further extend the life of micro satellites in operation in space. A set of specially design chip-sized microthrusters
receiving compressed air at various pressures have been tested to demonstrate the functionality in terms of thrust, nozzle performance and
chamber effectiveness. Both sea level and vacuum level tests have been
conducted enabling understanding of the effect of design parameters on
the micro nozzle mass generation rate and chamber performance. As
popular propellants like argon, helium, nitrogen, nitrous oxide, hydrogen, ammonia, and carbon dioxide are widely used in cold gas microthrusters, this present study using compressed air would allow us to
derive data for wide application in CGP design.
The corresponding equations used to calculate the theoretical value
of the Mach number, temperature, pressure, jet velocity at the exit of
the microthruster are given in Appendix A, together with the choked
mass flow rate, thrust produced, characteristic velocity, thrust coefficient, and specific impulse. The above assumptions apply in the theoretical calculations. In the case of numerical simulation and experimental study, shock waves and perturbations have been observed. The
amount of thrust produced by the microthruster chip depends on the
mass flow rate, exit jet velocity and the pressure at the nozzle exit.
The prime influential factor over the expansion ratio (ε) is the ratio
of the chamber pressure to the exit pressure of the nozzle. To achieve a
high exit velocity (Ve) and ultimately high thrust (F), the chamber
temperature (Tc) must be high, the ratio of the exit pressure (Pe) to the
chamber pressure (Pc) should be small, the molecular mass (M) of the
used gas should be low, and the specific heat capacity (γ) should preferably be lower, as it does not influence the exit jet velocity much. The
expansion ratio is selected based on the requirement of a vacuum level
operation. The expansion ratio of nozzles should be less than 15 for sea
level conditions and in the range of 20–400 for vacuum conditions for
optimum performance. But at the expansion ratio of 20–400, the chip
will require more space so there must be some trade-off between the
performance of the nozzle and the expansion ratio. Apart from this, a
standard nozzle has a semi divergent angle of 15° but at the micro level,
the semi divergent angle is increased to 28° as per the previous literature review [18,21]. Another reason for using 28° semi-convergent and
semi-divergent angle is to test the performance of the liquid microthruster chip using feed gas as propellant (in the event that the micro
satellite runs out of liquid fuel and will only be driven by the leftover
feed gas in the system). Hence, for the current study, the expansion
ratio of 15 is used with 28° of semi-convergent and semi-divergent
2. Design and numerical model
The focus of our experimental study is a microthruster designed as a
chip as shown in Fig. 3. The micro nozzle has been fabricated with an
expansion ratio of 15, which is the practical range for experiments simulating actual space conditions [16,17]. Previous literature suggests
that the semi divergent and semi convergent angles for the microthruster should be close to 28° so as to compensate for the dominating
viscous effect of the propellant over the mean free path of the propellant molecules [18,19]. Kundu et al. [18] reported that the hydraulic
diameter of the inlet should be such that the flow must not be interrupted due to friction dominance in the micro-level flow passage [18].
For the present study, a microthruster chip has been fabricated as a
three layer assembly, bound together with epoxy glue. The top most
layer is made of acrylic with the gas inlet hole at the top. The next two
layers are made of SS 304 stainless steel, which has good corrosive
resistance property for water and aqueous environment well below
425 °C [20]. All the three layers are bound together with J-B Weld, part
number 8265S epoxy glue. This epoxy glue is recommended for gluing
acrylic with stainless steel. The actual figure of the microthruster chip is
shown in Fig. 3.
The microthruster width is intentionally made wider than its length
for clamping and to ensure no leakage through the glued layers of the
composite microthruster. The dimensions of the microthruster are
Fig. 3. Actual microthruster chip.
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Table 1
Dimensions of microthruster.
Inlet diameter
Chamber width
Chamber length
Throat width
Exit width
Chamber depth
Semi convergent
Semi divergent
Expansion ratio
Wi (μm)
500
Wc (μm)
3000
LV (μm)
8000
Wt (μm)
60
We (μm)
900
Wd(μm)
100
Angle, α (°)
28
Angle, β(°)
28
ε
15
microthruster. To ensure no compressed air leakage from the system, a
PDMS (Polydimethylsiloxane) material of 5 mm × 5 mm × 4 mm size
has been securely fastened between the microthruster platform holder
and the mouthpiece of the microthruster.
Force measurement is done using a micro force sensor, which is
aligned to the exit of the micro nozzle using an XYZ positioner. The
micro force sensor is cabled to the charge meter. Based on the manufacturer’s prescribed standards for best results, charging of the charged
meter is required for at least an hour. A control valve is used to set
various pressure conditions upstream of the microthruster. The maximum pressure is set to 8 bar, and it is controlled by an in-built safety
system. A sponge wafer is placed beneath the microthruster and the
sensor holding platform to arrest any kind of external vibrational disturbances on the micro force sensor reading. For sea level testing conditions, the complete setup is placed inside the acrylic test box to nullify
atmospheric noise and ensure high integrity of recorded data. For
testing under vacuum conditions, the complete microthruster platform
along with the micro force sensor and the three-axis platform are placed
inside the vacuum chamber.
angle. Theoretical calculations help to obtain approximate values for
early design but computational fluid dynamics (CFD) modelling is relied upon to obtain detailed results.
2.2. Numerical model and its parameters
A model of the fabricated microthruster has been developed with
the true dimensions, and simulation has been performed using the
commercial ANSYS Fluent [22] package using various inlet pressure
and environmental conditions. The k-ε turbulence model is selected as
it is the most common CFD model used to simulate mean flow characteristics for turbulent flow conditions. In addition, the k-ε model is
able to capture shock and discontinuity in the flow through the micro
nozzle of the microthruster. The aero-thermodynamic properties of the
micro nozzle at various inlet pressure conditions have been simulated,
after mesh independence testing, and compared with the experimental
results. The properties of interest are pressure distribution, velocity
profile, temperature distribution, and the corresponding Mach number
distribution in the micro nozzle. The theoretical thrust value derived
from the simulation results is then set as a benchmark for a comparative
study on the experimental thrust value obtained by the designed microthruster.
Eight cases have been simulated and details are shown in Table 2.
3.1. Leak test
Because the microthruster is to be tested under pressure conditions
simulating sea level and vacuum, leak tests are needed to ensure the
integrity of the microthruster assembly together with the associated
interconnects around the microthruster, the sensors, the feed pump and
the test chamber. Liquid immersed type of leak test has been performed
at 5 bar pressure to test the integrity of bonded layers of the microthruster. Tests are repeated at various pressure conditions to ensure no
leakage throughout the working pressure range.
2.3. Boundary conditions
Boundary conditions have been set for sea level testing and vacuum
condition testing. In addition to that, solutions for pressure, temperature, Mach number and velocity vector are obtained using convergence
criteria residual of 1e-6. The complete solver set-up details are tabulated in Table 3.
3. Experimental set-up and measurements
3.2. Thrust and pressure measurements
Experimental set-ups for sea level testing and vacuum testing are
shown in Fig. 4 and Fig. 5, respectively. The experimental rig has
various components such as an MGF portable compressor with 8 bar as
maximum achievable pressure; two pressure gauges to monitor the
inline pressure and tank pressure with a measurement range of 0 bar to
12 bar; control valve to regulate various input pressure conditions;
1.6 mm and 4 mm tubing connecting thruster chip to compressor, respectively; PDMS (substrate of dimension 5 mm × 5 mm × 4 mm) to
avoid leakage; thruster and sensor holder platform with three axis adjustable micro gauge; Kistler 9207 model force sensor to measure
thrust; Kistler 5015 charge meter; Agilent (DSO3102A) digital storage
oscilloscope; and soft sponge to arrest any kind of vibration beneath the
platform and acrylic box. The complete setup is placed inside an acrylic
box for sea level testing to nullify external noise effect. For vacuum
testing setup, two additional components such as custom-made vacuum
test rig and the Vacsoundeco vacuum pump (model D28) are used as
part of the experimental rig.
The dimensions of the acrylic test box are 600 mm in length,
400 mm in width and 400 mm in height, and the dimensions of the
vacuum test rig are 350 mm in diameter and 300 mm in height. The
microthruster assembly is connected to a 1.6 mm input tubing and
connectors. A compressor is used to deliver compressed air to the
A Kistler force sensor (model 9207) and a charge meter (model
5015), recalibrated on-site, are used to measure thrust produced by the
microthruster. Data coming from the charge meter and sensor are sent
to the Agilent oscilloscope with digital storage capability. All data have
been recorded at a sensitivity of −118.8 pC/N. Pressure measurements
are recorded for pressure in the portable compressor tank; downstream
of the compressor tank; and the vacuum pressure inside the vacuum rig.
A schematic diagram of the experimental setup is shown in Fig. 6.
Table 2
Eight cases of numerical simulation.
924
Environmental conditions
Feed pressure, ΔP (bar) between chamber
pressure and ambient pressure
Sea level (1 bar absolute)
1 bar
2 bar
3 bar
4 bar
ΔP
ΔP
ΔP
ΔP
(Case
(Case
(Case
(Case
1)
2)
3)
4)
Vacuum condition (10 mbar
absolute)
1 bar
2 bar
3 bar
4 bar
ΔP
ΔP
ΔP
ΔP
(Case
(Case
(Case
(Case
5)
6)
7)
8)
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R. Ranjan et al.
A similar set-up used for sea level testing is used for vacuum testing.
The complete microthruster platform along with the micro force sensor
and three axis platform is placed inside the vacuum chamber.
Connections have been made and verified. Vacuum pump is switched
on to create vacuum inside the vacuum rig after closing the seal tightly
ensuring no vacuum loss. It must operate at slow and steady speed of 15
L/s or below to avoid damage to the chamber or pump [23]. The vacuum rig has a volume of 0.029 m3. A Kistler make coupling is used to
connect sensor cable from vacuum chamber to the charge meter. Data
has been recorded at various feed pressure conditions and at a vacuum
pressure of 10 mbar.
Table 3
Fluent solver setup.
Problem setup
General
Models
Materials
Boundary Conditions
Solution setup
Solution controls
Solution initialization
Solver type: density – based
2D Space: axisymmetric
Steady state
Energy equation: on
Viscous model: k-ε model with standard wall
treatment and compressibility effect
Ideal gas-air
Inlet pressure: varied for 8 cases
Set supersonic initial gauge pressure
Turbulent intensity: 5%
Turbulent viscosity: 10
Thermal: 300 k
No-slip wall
Operating pressure: 0
Outlet pressure; sea level – 1 bar, vacuum - 10 mbar
Run Calculation
Courant number: 0.5
Compute from: Inlet
Convergence criteria: 1e−6
Check case, enter number of iterations: 1000
Results
Graphics and animation
Post processing
4.2. Numerical results for sea level
In the following sections, the Mach and Velocity vector contours at
sea level for Case 1 to 4 are presented.
The pressure ratio, which is the difference in chamber pressure and
ambient pressure is least for Case 1, compared with Case 2, 3 and 4,
respectively for sea level testing. The amount of shock intensity is directly proportional to the pressure ratio. A high pressure ratio results
into a high intensity pressure shock as particles has to compensate more
pressure gradient to match the ambient pressure condition. The gradual
growth of shock intensity can be seen through corresponding Mach
number contour in Fig. 7, corresponding to the increasing pressure ratio
from Case 1 to Case 4.
In Case 1, the blue color contour appeared close to throat and further grown towards the outlet gradually from case 2 to case 4. In Fig. 7,
Mach number variation contour has been shown for Case 1 to 4. The
growth of Mach intensity variation can be seen by red color just after
nozzle throat region in Case 1 and starts to concentrate at center as it
moves towards the nozzle exit due to ambient pressure dominance with
back flow and shock intensity. This result is consistent for all four cases
of sea level testing. This is due to the fact that nozzle divergent angle is
higher than required for sea level condition. This kind of nozzle is defined as grossly over-expanded nozzle, where the nozzle exit pressure is
much lower than the ambient pressure.
4. Results and discussion
4.1. Sea level and vacuum measurements
For sea-level measurement, the experimental setup is placed inside
an acrylic box to shield it from external disturbances. The measurements are performed at various pressure conditions. The gap between
the sensor tip and the nozzle exit is set as 4 mm, based on past work
[18,21], and proper alignment is checked using the 3 axis positioner. As
the Mach number and velocity vector are key parameters affecting the
performance of the microthruster, detailed results are presented for
both vacuum and sea level testing.
Fig. 4. Setup for sea level testing.
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Fig. 5. Setup for vacuum testing.
perform well in terms of achieving higher Mach number at the micro
nozzle exit. It is due to higher divergent angle making micro nozzle
over-expanded and leading to higher divergence loss. This result has
concluded that the semi divergent angle should be less than 28° or
expansion ratio should be lower than 15, to operate at sea level condition and to get desired performance with minimum divergence loss.
Velocity vector shown in Fig. 8, gives clear indication of over-expansion
in divergent section of the micro nozzle. It results into high divergence
loss due to dominating reverse flow from sides of the micro nozzle wall.
A comparative study based on the numerical results for all the 4
cases of sea level testing has been discussed. The Mach number distribution is shown in Fig. 9 and found to be increasing gradually along
the nozzle axis in the convergent section and reached supersonic speed
near throat. As it has started to expand in the diverging section, it
Standard isentropic expansion density variation has been observed
for all 4 cases, gradually increasing from Case 1 to 4 and similar isentropic expansion pattern for temperature distribution has also been
found in results. The static temperature started to reduce and moved
towards exit gradually from Case 1 to 4. The back flow has been found
to be dominating with the increase in pressure ratio from Case 1 to Case
4 and suppressed the exit velocity at great extent, producing lower
thrust value at the exit. At throat section, the Mach number has been
found to be close to 1 near throat but dominating reverse flow restricted
its further growth immediately as it progressed towards the nozzle exit.
The same effect has been reported by velocity magnitude contour as
well in Fig. 8. Dominating back flow has been observed with increasing
back flow from nozzle wall side from Case 1 to Case 4, respectively.
Overall the results have shown that the micro nozzle did not
Fig. 6. Experimental setup for vacuum testing of the microthruster.
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Fig. 7. Mach Number variation at sea level from Case 1 to Case 4.
Fig. 8. Velocity vector variation at sea level from Case 1 to Case 4.
Fig. 9. Mach number along axis from Case 1 to Case 4.
Fig. 10. Mach number along wall from Case 1 to Case 4.
reduced gradually due to ambient back pressure dominance from outside of nozzle exit towards inside of nozzle exit from nozzle wall side.
Similar isentropic trends for pressure, temperature and density have
been observed for all the four cases. The Mach number drop in the
divergent section has been found to be faster along the nozzle wall than
the axis. It is due to the flow separation along the nozzle wall is more
dominating than along the axis. It can be seen in Fig. 10.
Static pressure has been found to be almost constant along the
nozzle axis in the convergent section and dropped down gradually at
the throat. It started to expand in the divergent section, as the ambient
back pressure induced flow separation along the nozzle wall gradually.
Similar trend of the pressure variation has been observed for Case 1 to
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Fig. 11. Mach Number variation in vacuum testing from Case 5 to Case 8.
Case 4. Back flow in the divergent section has been found to be faster
along the nozzle wall than the axis. Static temperature has been found
to be almost constant along the nozzle axis throughout the nozzle for
Case 1 and Case 2 but in Case 3 and Case 4, it started to drop at the
throat in the convergent section and gradually recovered in the divergent section. Similar trend of static temperature has been observed
for all the four cases of feed pressure. Even along the nozzle wall similar
trend has been repeated, the temperature recovery in the divergent
section has been found to be faster than along the axis. It is due to the
over expansion of the micro nozzle. To conclude the argument, results
have suggested that the micro nozzle has not perform well in sea level
condition and has shown high divergence loss due to over expansion of
divergent section of the micro nozzle.
pressure is 2 bar and absolute outlet pressure is set as 10 mbar. The back
flow is found to be lower along the nozzle axis and more along the
nozzle wall of the divergent section. The Mach number is found to be
4.597. Similar effects are reported by velocity magnitude and static
pressure contours. Results show that the micro nozzle performed well in
terms of obtaining high Mach number at the nozzle exit with further
lower divergence loss than Case 5.
Case 7 is defined as 3 bar feed pressure, where absolute inlet pressure is 3 bar and absolute outlet pressure is set as 10 mbar. The back
flow is found to be almost nil at the nozzle exit. The Mach number is
found to be 4.668 with no reverse flow in the divergent section. Results
show that the micro nozzle performed well in terms of obtaining high
Mach number at the nozzle exit.
Case 8 is defined as 4 bar feed pressure where absolute inlet pressure is 4 bar and absolute outlet pressure is set as 10 mbar. There is no
back flow observed at the nozzle exit or along the wall of the divergent
section. The Mach number is found to be 4.723 and the reverse flow
effects are nil in divergent section. Results show that the micro nozzle
performed optimally in terms of obtaining high Mach number at the
nozzle exit with no divergence loss at all.
The temperature reduction of 240 K did not affect the nozzle performance for air as propellant but for liquid propellant it may be undesirable as it could result in icing at the nozzle exit. Overall the micro
nozzle performed well in all the four cases for vacuum conditions because the nozzle behaved as over-expanded in Case 5, optimum for Case
6 and under-expanded for Case 7 and Case 8 but with minimum
4.3. Numerical results for vacuum environment
Mach number contours for Case 5 to Case 8 are shown in Fig. 11.
Case 5 is defined as 1 bar feed pressure, where absolute inlet pressure is
1 bar and absolute outlet pressure is set as 10 mbar at 0 bar absolute
operating pressure condition. The back flow is found to be less dominating along the nozzle axis and more along the nozzle wall of the
divergent section. The Mach number is found to be 4.485. Similar effect
has been reported by static pressure contour as well. Results show that
the micro nozzle has performed well in terms of obtaining high Mach
number at the nozzle exit at lower divergence loss.
Case 6 is defined as 2 bar feed pressure, where absolute inlet
Fig. 12. Velocity vector variation in vacuum testing from Case 5 to Case 8.
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temperature has been found to be very critical for vacuum condition
testing throughout the nozzle. In the case of compressed air as propellant, no freezing has been observed at the nozzle exit even at sudden
temperature drop but it could be very critical in the case of water as
propellant.
4.4. Numerical model result validation with experimental results
4.4.1. Sea level
Both thrust and specific impulse for Case 1 to Case 4 of sea level
testing are found to be quite close to the simulated results of the corresponding cases as shown in Fig. 15. The error in the data is higher at
lower pressure difference of 1 bar and 2 bar due to the higher ambient
pressure than pressure at throat, which caused dominating reverse flow
in the nozzle divergent section. It has reduced gradually at high feed
pressure of 3 bar and 4 bar. It is due to the fact that feed pressures at the
nozzle throat have increased and ambient pressure remained same.
Experimental thrust values of 0.32 mN at 1 bar feed pressure to 1.12 mN
at 4 bar feed pressure have been reported in sea level testing.
Fig. 13. Mach number along axis from Case 5 to Case 8.
4.4.2. Vacuum and sea level result comparison
Thrust values of 0.8 mN at 1 bar feed pressure to 2.24 mN at 4 bar
feed pressure have been reported for vacuum testing and shown in
Fig. 16. The thrust achieved in vacuum condition has been found to be
almost double the value of thrust achieved in case of sea level for the
corresponding feed pressures. The microthruster performed optimally
in case of vacuum condition with no divergence loss.
Both thrust and specific impulse for all the four cases of vacuum
testing have been found to be quite close to the simulated results for the
corresponding cases 5 and 6, which is at lower feed pressure. At higher
feed pressure as in case of Case 7 and Case 8, the difference between
experimental and simulation result increased. This difference looks
significant in Fig. 17 due to the noise and perturbation that affect the
experimental readings every time the data are recorded. As these
measurements are in micro Newton range, a small perturbation in the
surroundings may adversely affect the results. The data have also been
recorded in continuous mode operation of the vacuum pump and more
disturbances occur inside the vacuum chamber affecting the sensor
reading. The error in the data is lower at lower pressure and increases
gradually due to the additional noise produced by high flow rate and
pressure build-up in the vacuum chamber from 10 mbar to 60–80 milli
bar in Case 7 and 80–100 mbar in Case 8. The graph shown in Fig. 18
shows the nozzle efficiency. It has been found to be better in vacuum
Fig. 14. Mach number along wall from Case 5 to Case 8.
divergence loss. Velocity vector graphs for vacuum testing from Case 5
to Case 8 are shown in Fig. 12, which are supported by the previous
explanation of Mach variation and micro nozzle divergence performance. As seen in Fig. 11 and Fig. 12, particles and disturbances are
moving faster than the medium could propagate and the fluid near the
disturbance could not react before the disturbance arrived, which resulted into shock and discontinuity formation.
A comparative study, based on the numerical results of all the 4
cases of vacuum environment testing from Case 5 to Case 8, are shown
in Fig. 13 and Fig. 14, respectively. Mach number is found to be increasing gradually along the nozzle axis in the converging section,
reached supersonic speed at the throat and further reached 4.7 at the
nozzle exit in divergent section. Similar trend is observed for all the
four cases of feed pressures. Along the nozzle wall, the Mach number
drops gradually in the divergent section due to the flow separation
along the nozzle wall but not as significant as in the case of sea level
testing for similar feed pressure conditions.
Static pressure has shown standard trend as shown under ideal
isentropic conditions along the nozzle axis throughout the micro nozzle.
Similar trend has been observed for all the four cases of feed pressure.
Along the nozzle wall, standard isentropic expansion trend has been
repeated due to lower ambient pressure of vacuum condition. Static
Fig. 15. Thrust and specific impulse vs pressure difference for case 1 to case 4.
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Fig. 16. Thrust and specific impulse vs pressure difference for Case 5 to Case 8.
Fig. 18. C* efficiency and thrust correction factor vs pressure difference.
system that can be used in conjunction with liquid fuel. The system has
various merits such as non-toxicity, easy to use, and low leakage concern over other propulsion systems. This is the first attempt that reports
that the life of a liquid fueled based propulsion system in a microsatellite can be enhanced even when the system runs out of liquid fuel.
A CFD model for the same has also been developed and the experimental results are used to validate it. Thrust values are obtained ranging from the micro to milli-Newton range so as to fulfil the requirements of attitude and station keeping for the CubeSat of 1–50 kg dry
mass range. Under vacuum conditions, thrust values of 0.8 mN at 1 bar
feed pressure to 2.24 mN at 4 bar feed pressure have been achieved.
The result of sea level testing has shown dominating boundary
layers effects under ambient conditions and the micro nozzle geometry
suitable for vacuum cannot be effective under atmospheric conditions.
The experimental results for all the eight cases have shown closest
agreement with the simulation results and relevant results have been
reported. The reason for variation in error percentage in all the cases
has also been discussed.
The Mach number and velocity vector contours have provided information related to growing shock movement from the nozzle throat
towards the nozzle exit with increase in pressure ratio. The results also
helped to understand the divergence loss phenomena due to over expansion of the nozzle exit in sea level testing.
In the case of higher pressures of vacuum testing, oscillations have
been produced by high flow rate and pressure increase in the vacuum
chamber, due to increase in gas volume in chamber from 10 mbar to
60–80 mbar in Case 7 and 80–100 mbar in Case 8 have affected the
result and have been reported with the help of % error graph in Fig. 18.
Thrust values of 0.8 mN at 1 bar pressure difference to 2.24 mN at 4 bar
pressure difference have been reported for vacuum testing. It is approximately double the value of thrust achieved in case of sea level for
the corresponding feed pressures. This indicates that the microthruster
would perform optimally under vacuum conditions where it is meant to
be used. The amount of thrust and specific impulse produced here is in
line with the thrust requirement of the microsatellites for 1–50 kg category [21].
Fig. 17. % Error vs pressure difference.
condition and is less efficient at sea level testing condition due to the
higher divergent loss at sea level condition.
Thrust correction factor is found to be 1.8–1.4 for the sea level
testing and 1 to 0.6 for vacuum testing, shown in Fig. 18. It represents
the ratio of actual thrust to the idealized thrust value. Lower thrust
correction has been required in case of vacuum testing and higher for
the sea level condition to ensure better performance. It also indicates
that the microthruster performed optimally in vacuum condition, where
these microthrusters are actually going to be used.
5. Conclusion
The present work focuses on CGP system development, utilization of
feed gas using same liquid fueled thruster and its experimental testing
in simulated vacuum condition and sea level condition at various feed
pressure conditions. An attempt has been made to develop a CGP
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Appendix A. Equations
Thrus,
̇
F = mVe
+ (Pe−Pa) Ae
(1)
Specific impulse,
Isp =
F
= Cf ∗C ∗
ṁ
(2)
Specific impulse at sea level
(P −P ) ∗Ae ⎞
Isp = Ve + ⎛ e a
ṁ
⎝
⎠
(3)
Specific impulse at vacuum,
P ∗A
C ∗∗Pe ∗∊ ⎞
Isp = Ve + ⎛ e e ⎞ = Ve + ⎛
Pc
⎝ ṁ ⎠
⎠
⎝
⎜
⎟
(4)
Thrust coefficient,
⎛ γ+1 ⎞
2γ ⎛
2 ⎞⎝ 2(γ − 1) ⎠
Pe ⎛
γ ∗ ⎛⎜
⎟
∗
1−⎛ ⎞⎝
⎜
γ −1 ⎜ ⎝ Pc ⎠
⎝ γ + 1⎠
⎝
⎜
Cf =
⎟
γ−1
⎞
γ ⎠⎞
⎟⎟
⎠
(5)
Characteristic velocity,
RTc
C∗ =
γ∗
γ+1
⎛
⎞
2
⎝ 2(γ − 1) ⎠
γ+1
( )
(6)
Expansion ratio,
(
(
)
∊=
2
γ+1
1
γ−1
)∗
( )( )
γ+1⎛
Pe
⎜1−(
)
γ−1
Pc
Pc
Pe
1
γ
( γ−γ 1 ) ⎞
⎝
⎟
(7)
⎠
Jet/exit velocity,
⎛
Ve =
2∗γ ∗Ro ∗Tc ⎛ ⎛ Pe ⎞⎝
⎜1−
(γ −1) M ⎜ ⎝ Pc ⎠
⎝
⎜
⎟
γ−1
⎞
1 ⎠⎞
⎟
⎟
⎠
(8)
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Appendix B. Micro force sensor
[3] Williams C, Doncaster B, Shulman J, 2018 Nano/Microsatellite; 2018.
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micro propulsion for small satellites; 2006.
[5] Rhee MS, Zakrzwski CM, Thomas MA, Highlights of nanosatellite propulsion development program at NASA-Goddard space flight center. In: Proceedings of the
AIAA/USU conference on small satellites, Logan, UT, Aug 21-24, 2000.
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