Determination of shock losses and pressure losses in ug mine openings
Team Dorado Cold Gas Thruster Report Final
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Cold Gas Thruster
Design, Build, Test
AAE 439: Extra Credit Project
Team Dorado
Saphal Adhikari, Claire Alexander, Alicia Benhidjeb-Carayon, and Julian Wang
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Table of Contents
Design and Thruster Analysis:.........................................................................................3
Design Requirements ..................................................................................................3
Known Conditions and Assumptions..........................................................................3
Design Background.....................................................................................................3
Change in Altitude ......................................................................................................4
Nozzle Design ............................................................................................................7
Stress analysis..............................................................................................................8
Overall Thickness .......................................................................................................9
Thrust Chamber Design..............................................................................................9
Overall Thruster Design and Dimensions .................................................................11
Test Results:..................................................................................................................13
Test Analysis: ................................................................................................................13
Theoretical Test Analysis:..............................................................................................15
Conclusions and Considerations:...................................................................................16
Conclusions about Design from Testing ...................................................................16
Comparison of Cold Gas Thruster and Hydrogen Peroxide Thruster........................16
Consider injecting reacting gas into the thrust chamber.............................................17
Aluminum Thruster Heat Transfer Analysis..............................................................21
Steel Thruster Heat Transfer Analysis .......................................................................22
Heat Transfer Analysis Discussion............................................................................23
Use as a main propulsion system...............................................................................23
References:....................................................................................................................24
Appendix: .....................................................................................................................25
Value Table(s) ...........................................................................................................25
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Design and Thruster Analysis:
Design Requirements
Design Requirements
Propellant Air
Operating Temperature TBD
Operating Altitude 86km – 97km
Thrust 10 lbf
Chamber Pressure 100 psia
Thruster Diameter Less than 3 in
Thruster Length Less than 3 in
Nozzle geometry 80% bell nozzle
Known Conditions and Assumptions
Working Propellant: Air (k = 1.4, R = 1716 ft/s)
P1 = Chamber Pressure = 100 psi
P2 = Exit Pressure = 0.4*Pambient = 5.88 psi
T1 = Chamber Temperature = 536.4 R
Max Dimensions: 3x3x3 inches cubed
Altitude (km) Pressure (Pa) Pressure (psia)
80 0.945 1.37x10-4
86 0.669 9.70x10-5
87 0.623 9.04x10-5
88 0.577 8.37x10-5
89 0.531 7.70x10-5
90 0.485 7.03x10-5
91 0.439 6.37x10-5
92 0.393 5.70x10-5
93 0.347 5.03x10-5
94 0.301 4.37x10-5
95 0.255 3.70x10-5
96 0.209 3.03x10-5
97 0.163 2.36x10-5
100 0.025 3.63x10-6
Table 1: Atmospheric pressure as a function of altitude (Source: NASA GSFC)1
Design Background
The design of the thruster is to perform optimally at an altitude range of 86 km to 97 km.
However since the thruster is also expected to undergo testing at sea level conditions, we
must consider if a thrust capable of performing optimally at an altitude range of 86 km to
97 km is even possible.
In order for the thruster to operate optimally at those conditions, the exit pressure of the
thrust must equal to that of the ambient conditions. In this case, the thruster would have
to accelerate its propellant to near vacuum conditions.
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Based on what Professor Anderson said in class, a thruster can have backflow occur if
the thruster is too over expanded. Therefore if the Pexit < 0.4*Pambient, our thruster flow
would face separation. Thus any test of our optimally expanded thruster would not
provide any useful data at sea level conditions because it would be too over expanded.
Our design will be 100% efficient and from the cold gas operation test, we can then
determine what is the C*
and Cf efficiencies.
Also looking at literature of previous cold gas thruster test, the temperature of the supply
air was at room temperature (298 K = 536.4 R).
Change in Altitude
Assuming that flow from the chamber to exit is isentropic; we can assume that the
chamber pressure is stagnating while the exit pressure is static.
Exit Mach = 2.4970
Using Mach number, we can use the isentropic area expansion equation to find
expansion ratio:
Eqn. 1
Ae/At = 2.6294
However since we are ranging from an altitude of 86 km to 97 km, pressure will change
and therefore affect our performance.
Knowing how pressure changes with altitude, we can calculate C*
, Cf, Isp, and Mass
Flow.
C*
was calculated using the following equation:
Eqn. 2
The figure below details the change in C*
with respect to altitude.
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Figure 1: C* vs Altitude
C*
will be constant because it is only a function of Tchamber and Tchamber = 536.4 R.
Cf was calculated using the following equation:
Eqn 3.
The figure below details the change in Cf with respect to altitude.
Figure 2: Cf vs Altitude
Cf changes with altitude because P3 (ambient pressure) changes with altitude. The higher
the altitude, the lower the pressure, thus the term P2-P3 becomes larger, making Cf larger.
Isp was calculated using the following equation:
86 88 90 92 94 96 98
1400
1400.5
1401
1401.5
1402
1402.5
Altitude [km]
C*[ft/s]
86 88 90 92 94 96 98
1.4084
1.4084
1.4084
1.4084
1.4084
1.4084
1.4084
1.4084
1.4084
1.4084
1.4084
Altitude [km]
ThrustCoefficient
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Eqn. 4
The figure below details the change in Isp with respect to altitude.
Figure 3: Isp vs Altitude
Since Isp is directly related to Cf, as Cf increases Isp increases. Therefore as altitude
increases, Isp also increases. From the figure above, the change in Isp isn’t much because
the change in pressure of the atmosphere is negligible since its already so thin at those
altitude.
Mass flow can be calculated using the following equation:
Eqn. 5
The figure below details the change in Thrust with respect to altitude.
Figure 4: Mass Flow vs Altitude
Since mass flow is directly related to Isp and since thrust is constant, as Isp goes up,
mass flow goes down. Therefore you need less mass flow to achieve the same desired
86 88 90 92 94 96 98
61.2844
61.2844
61.2844
61.2844
61.2844
61.2844
61.2844
61.2844
Altitude [km]
Isp[secs]
86 88 90 92 94 96 98
0.1632
0.1632
0.1632
0.1632
0.1632
0.1632
0.1632
Altitude [km]
MassFlow[lbm/s]
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thrust. That means if someone wants to use a thruster to maintain a spacecraft’s altitude,
they better operate the station keeping maneuvers higher rather than lower in the
atmosphere, otherwise they will be wasting more propellant.
Nozzle Design
Since the thruster is designed to be operating at a range of 86 to 97, the design point of
the thruster will be at 92 km, the average of the two boundary conditions.
With a design point of 92 km, the performance of the thruster can be determined:
Performance at Operating Point
Cf 1.4084
C* 1401.14 ft/s
Isp 61.2844 secs
Mass Flow 0.1532 lbm/s
Table 2: Performance of Thruster at Operating Point
The geometry of the thruster can then be determined using the following equations:
Eqn. 6
Eqn .7
Thruster Geometry
At 0.071 in^2
Rt 0.15033 in
Ae 0.18669 in^2
Re 0.2437 in
Lcone 0.3485 in
Table 3: Thruster Geometry
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Stress analysis
Assumptions:
o Thin wall pressure vessel
o Radius and thickness remains constant
o Stress distributions throughout wall thickness is constant
Figure 5: Visual of stresses in a thin walled pressure vessel
Variables:
o σa = axial stress (longitudinal stress)
o σh = hoop stress (latitudinal stress)
o Pc = chamber pressure
o Rc = chamber radius
o t = thickness of vessel
o CR = contraction ratio
o Ac = Area of the chamber
o At = Area of the throat
o Θ = angle of pressure force
Use the maximum chamber pressure: Pc=100psia
The force of the chamber pressure acts on the wall at an angle perpendicular to the wall
in the longitudinal direction. (see figure below)
Figure 6: visual of finding axial stress
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Find the Axial stress using Trigonometry:
𝜎 𝑎 = 𝑃𝑐 tan(𝜃) Eqn. 8
𝜎 𝑎 = 100𝑝𝑠𝑖𝑎 tan(45°)
𝝈 𝒂 = 𝟏𝟎𝟎𝒑𝒔𝒊𝒂
Find hoop stress (equation from Textbook: Mechanics of Materials):
𝜎ℎ = 2𝜎 𝑎 Eqn. 9
𝜎ℎ = 2 ∗ 100𝑝𝑠𝑖𝑎
𝝈 𝒉 = 𝟐𝟎𝟎𝒑𝒔𝒊𝒂
Overall Thickness
Thickness determined based on the stress analysis.
(from Mechanics of Materials):
𝜎ℎ =
𝑃𝑐∗𝑟𝑐
𝑡
, 𝜎 𝑎 =
𝑃𝑐∗𝑟𝑐
2∗𝑡
Eqn. 10 &11
Find CR (contraction ratio) for thickness calculation:
𝐶𝑅 =
𝐴 𝑐
𝐴 𝑡
Eqn. 12
We decided to go with a Contraction Ratio of 10. A larger Combustion Ratio is necessary
based on the small overall size of the thruster and the fact that the fuel that will be used
is cold gas.
𝑪𝑹 = 10
Use design parameters to find dimensions of the chamber:
𝐴 𝑐 = 𝐴 𝑡 ∗ 𝐶𝑅 Eqn. 13
𝑨 𝒄 = 𝟎. 𝟕𝟏 𝒊𝒏 𝟐
𝑟𝑐 = √
𝐴 𝑐
𝜋
Eqn. 14
𝒓 𝒄 = 𝟎. 𝟒𝟕 𝒊𝒏
𝑫 𝒄 = 𝟎. 𝟗𝟓 𝒊𝒏
Re-arrange stress formulas to find thickness:
𝑡 =
𝑃𝑐∗ 𝑟𝑐
𝜎ℎ
Eqn. 15
𝑡 =
100𝑝𝑠𝑖𝑎 ∗ 0.47𝑖𝑛
200𝑝𝑠𝑖𝑎
𝒕 = 𝟎. 𝟐𝟑𝟓 𝒊𝒏
Thrust Chamber Design
Stated in the project parameters, we must design the thruster to be no more than 3
inches in length total. Therefore, with a nozzle length of 0.3485 inches, the chamber
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length can only be as much as 2.6515 inches. We will round this number down and have
a chamber length of 2.5 in.
𝑳 𝒄 = 𝟐. 𝟓 𝒊𝒏
We can now find the combustor aspect ratio:
𝐶𝐴𝑅 =
𝐿 𝑐
𝐷𝑡
Eqn. 17
When Dt is the diameter of the throat.
𝐷𝑡 = 2 ∗ 𝑟𝑡 Eqn. 18
𝐷𝑡 = 0.15 𝑖𝑛 ∗ 2 = 0.3 𝑖𝑛
Therefore:
𝐶𝐴𝑅 =
2.5 𝑖𝑛
0.3 𝑖𝑛
= 𝟖. 𝟑𝟑
Injector Design
The design of the Injector was based on the parameters given for the gas supply hose as
well as the dimensions for the chamber. The inside of the injector chamber will be threaded
using a ½’’ NPT threading. The gas supply hose will have a diameter of 0.5 inches.
Therefore, the injector chamber diameter is as follows:
𝑫𝒊𝒄 = 𝟎. 𝟓 𝒊𝒏
The injector will then expand to the diameter of the chamber and fasten around the
outside of the chamber. The two will be fastened using a NPT threading. Therefore, the
overall injector diameter is as follows:
𝐷𝑖𝑜 = 2 ∗ 𝑟𝑐 + 2 ∗ 𝑡 Eqn. 19
𝑫𝒊𝒐 = 𝟏. 𝟒𝟏 𝒊𝒏
An illustration is provided below (injector = red, chamber = blue):
Figure 7: Injector Diagram
The horizontal length of the injector parts will not be counted towards the overall 3 inch
parameter because the injector will mostly be surrounding the camber and the supply
hose. Therefore, the length of the injector parts is determined based on need rather than
calculations.
𝑳 𝟏 = 𝟎. 𝟓 𝒊𝒏
𝑳 𝟐 = 𝟏 𝒊𝒏
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Overall Thruster Design and Dimensions
Figure 6: Side View
Figure 7: Isometric View
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Nozzle:
θi – inflection angle
θe – exit angle N/A
Lbell 0.3485 in
Approach radius 1.5rt 0.225 in
Expansion radius 0.4rt 0.06 in
At 0.071 in2
rt 0.15 in
Ae 0.186 in2
re 0.244 in
Lnozzle 0.3485 in
t 0.235 in
Table 6: Nozzle Dimensions
Chamber:
Ac 0.5 in2
rc 0.43 in
Lc 2.5 in
t 0.239 in
Table 7: Chamber Dimensions
Injector:
L1 0.5 in
L2 1 in
Dio 1.41 in
Dic 0.5 in
t 0.235 in
Table 8: Injector Dimensions
13. Test Results:
The following is the test procedure for the cold gas thruster.
Figure 8: Testing Setup
i. Align and mount the cold gas thruster on the thrust stand as shown in the picture above. It
should be checked carefully if the thruster is secured properly or not.
ii. Clear any tool and instruments on the thrust stand before running the test.
iii. Check the pressure valve of the pressure supply. If the valve is open then close it.
iv. Attach the pressure supply to the cold gas thruster via NPT fittings.
v. Turn on the pressure supply valve and maintain a steady pressure of 100 psi.
vi. Record the exact pressure value supplied.
vii. Record the mass flow from the supply tank
viii. Record the thrust data recorded by the thrust stand.
ix. Turn off the pressure supply.
x. Repeat the procedure 5 times.
If the experiment was performed, the experimental data would have consisted of thrust values for
corresponding chamber pressure and mass flow
Test Analysis:
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The chamber will attain the same pressure as the pressure supply. It was assumed that there will be no pressure
drop between the camber and the supply.
The experimental thrust values will be compared to the design thrust value of 10 lbf. The difference between
experimental thrust and theoretical thrust will determine the accuracy of our design. Furthermore, performance
parameters will be calculated at test conditions and will be scaled to the flight conditions.
By using the chamber pressure (p1), throat area (At) and the total mass flow (𝑚̇ ) the value of effective exhaust
velocity (c*) will be found.
Eqn. 20
Then, the value of thrust coefficient (CF) will be calculated by using the experimental thrust value (F), chamber
pressure (p1) and throat area (At).
Eqn. 21
The Isp of thruster is then calculated by using effective exhaust velocity (c*), thrust coefficient (CF) and standard
gravity (g0).
Eqn. 22
The performance of the thruster at different altitude (design altitude) where the flow is perfectly expanded (p2
= p3) is calculated by scaling the thrust coefficient value.
Eqn. 23
Where,
p2 = p3 = pambient
Effective exhaust velocity (c*) is a function of geometry and will not change with altitude. Then, the scaled Isp
is calculated by using new value of thrust coefficient.
There will be inefficiencies in the thruster due to pressure loss, friction loss, etc. The effective exhaust velocity
efficiency, thrust coefficient efficiency and overall efficiency will be calculated by using experimental values and
theoretical values. The theoretical values are calculated by using theoretical design parameters.
𝜂 𝑐∗ =
𝑐∗,𝑎𝑐𝑡𝑢𝑎𝑙
𝑐∗,𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
Eqn. 24
𝜂 𝐶𝐹 =
𝐶𝐹,𝑎𝑐𝑡𝑢𝑎𝑙
𝐶𝐹,𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
Eqn. 25
𝜂 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =
𝐼𝑠𝑝,𝑎𝑐𝑡𝑢𝑎𝑙
𝐼𝑠𝑝,𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙
Eqn. 26
We were not able to test our design due to the semester time constraint as well as some difficulty we
ran into when trying to get our design manufactured. Therefore, we do not have any data or
conclusions about the design to discuss.
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Theoretical Test Analysis:
Due to time constraints, the thruster was not able to undergo experimental testing. Therefore a
theoretical test was conducted to examine what kind of performance could have been expected if
the experimental test was conducted.
Therefore using the same geometry and mass flow rate but setting the ambient pressure to 14.7 psi,
the following values are the expected outcome of the experimental test:
Theoretical Performance at SL
C* 1400.00 ft/s
Cf 1.12
Isp 48.70 secs
Thrust 7.46 lbf
Table 9: Theoretical SL Performance
However the theoretical performance values obtained would be the ideal performance at sea level.
So the theoretical and experimental values will be off by a factor of .90~.98% due to efficiency
factors.
Comparing the performance at the operating point and at sea level, it can be seen that performance
across every spectrum is worse at sea level than at the operating point. The main contributor to this
decline in performance is the ambient pressure. As ambient pressure decreases, the thruster
performance will increase. Therefore is it unsurprising that at the operating point, the thruster will
perform better.
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Conclusions and Considerations:
Conclusions about Design from Testing
We were not able to test our design due to the semester time constraint as well as some difficulty we
ran into when trying to get our design manufactured. Therefore, we do not have any data or
conclusions about the design to discuss.
Comparison of Cold Gas Thruster and Hydrogen Peroxide Thruster (HPT)
The cold gas thruster and the HPT were compared to examine which system is better. In order to
begin the comparison, the cold gas thruster must be resized to match that of the HPT. The HPT
case study thruster has a different operating temperature, pressure, and exit pressure, all of which
will contribute to a different performance. Therefore the new cold gas thruster must match the case
study. The new cold gas thruster will have the flowing performance parameters:
Resized Cold Gas Thruster Parameters
F 10 lbm
P1 150 psi
P2 5 psi
T1 850 K
Table 10: Resized Cold Gas Thruster Parameters
The new operating temperature was centered on the HPT’s max operating temperature. Based on
the information above, the cold gas thruster new performance was examined below:
Resized Cold Gas Thruster Performance
C* 2370 ft/s
Cf 1.54 psi
Isp 113 psi
mair 0.0884 lbm/s
Table 11: Resized Cold Gas Thruster Performance
Comparing the new cold gas thruster’s performance with the HPT case study’s performance, it is
clear that the HPT case study outperforms the cold gas thruster based on Isp. Given the same
operating conditions, the cold gas thruster’s Isp was still ~75% of the HPT’s Isp.
The reason why the HPT outperformances the cold gas thruster is due its specific heat ratio.
Examining the equations for Cf and C*, there are two main gas properties that affect Isp, the
molecular weight of a gas and its specific heat constant. A greater molecular weight will cause a
decrease in Isp performance while a decrease in specific heat constant will cause an increase in Is
Since H2O2 has a greater molecular weight than air, the specific heat ratio of H2O2 must be lower
17. Cold Gas Thruster Project
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than that of air to a significant point that H2O2 is a better option than air. However no data can be
found on the specific ratio of H2O2, so this theory cannot be verified.
Methods to Increase Performance
The performance of the cold gas thruster can be easily increased by pre-heating the chamber gas by
transferring electrothermal heat from electrical resistors. By adding electrical resistors, the cold gas
thruster transforms into an electric propulsion device known as a resistojet.
The increase in performance can be modeled increasing the chamber temperature and then
calculating the new Isp of the thruster.
The increase in chamber temperature will lead to an increase in 𝐶∗
. Since Isp is directly related
with 𝐶∗
, an increase in chamber temperature will lead to an increase in Isp.
Assuming constant geometry, an operating altitude of 92 km where ambient pressure = 5.7e-05 psi,
and an original chamber temperature of 536.4 Rankine, the following graph was created:
Figure 9: Isp vs Chamber Temperature
Analysis was done if the thruster was created out of either steel or aluminum. The design
temperature of each material was taken into consideration in order to evaluate the max possible gain
in Isp due to electrothermal heating.
From a starting Isp of 61.28 seconds, the aluminum thruster can have its Isp increase upwards to an
Isp of 72.3 seconds, while the steel thruster can have its Isp increase upwards to an Isp of 93.09
seconds.
That means the aluminum thruster can experience a 17.98% boost in performance while the steel
thruster can experience a 51.91% boost in performance!
Taking the overall systems into account, discuss whether the designed thruster would be a good
alternative to HTP for the Nanolaunch 1200. Take into consideration the performance vs weight
and performance vs cost for the required duty cycle.
Consider injecting reacting gas into the thrust chamber
Setup Conditions
500 600 700 800 900 1000 1100 1200 1300
60
65
70
75
80
85
90
95
Chamber Temperature [Rankine]
Isp[secs]
Chamber Temp
Al Design Temp
Steel Design Temp
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Running CEA with LH2/LOX with the following conditions:
Chamber Pressure: 100 psi
Propellant: H2(L)
Oxidizer: O2(L)
O/F: Variable
Supersonic Area Ratio: 2.6294
O/F of the LH2/LOX system was based on the design temperature of the construction material.
Viewing the graph below:
Figure 10: Material Tensile Yield Stress vs Temperature
It is observed that Aluminum has a design temperature of ~ 350 F (809.7 R) and that Stainless Steel
has a design temperature of ~800 F (1260 R).
Calculations for thruster performances were made at the design point altitude of 92 km where
ambient pressure = 5.7e-05 psi and a desired thrust of 10 lbf is still maintained.
Running CEA
Since the thruster could be made of either aluminum or stainless steel, it is necessary to obtain the
O/F ratios that correspond to these two design temperatures to see the maximum performance of
each design. Therefore using CEA, a series of chamber temperature was created based on a variety
of O/F ratios.
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Figure 11: Chamber Temperature vs OF Ratios
Examining the graph above, the aluminum thruster would have a max O/F = 0.454 and the steel
thruster would have a max O/F = 0.7075
Performance Analysis
Aluminum Thruster Analysis
Examining the Aluminum Thruster first, with an O/F = 0.454, the thruster would have an:
Aluminum Thruster Properties
P2 7.836 psi
C* 5421 ft/s
Cf optimal 1.3301
Table 12: Aluminum Thruster Properties
Due to the exit pressure, the Cf correction term:
𝐶𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛
=
𝑃2 − 𝑃3
𝑃1
= 0.07836
Therefore,
𝐶𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙
= 𝐶𝑓 𝑜𝑝𝑡𝑖𝑚𝑎𝑙
+ 𝐶𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛
= 1.4085
𝐼𝑠𝑝 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 =
(𝐶𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙
) (𝐶∗
)
𝑔0
= 237.12 𝑠𝑒𝑐𝑠
With our desired thrust = 10 lbf,
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
600
800
1000
1200
1400
1600
1800
2000
2200
2400
O/F Ratios
ChamberTemperature[R]
LH2/LOX System
Chamber Temp
Al Design Temp
Steel Design Temp
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𝐹 = (𝐼𝑠𝑝 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙)(𝑚̇ )(𝑔0)
𝑚̇ = 0.04217
𝑙𝑏𝑚
𝑠𝑒𝑐𝑠
Steel Thruster Analysis
Examining the Aluminum Thruster first, with an O/F = 0.7075, the thruster would have an
Steel Thruster Properties
P2 5.969 psi
C* 6257 ft/s
Cf optimal 1.348
Table 13: Steel Thruster Properties
Due to the exit pressure, the Cf correction term:
𝐶𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛
=
𝑃2 − 𝑃3
𝑃1
= 0.05969
Therefore,
𝐶𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙
= 𝐶𝑓 𝑜𝑝𝑡𝑖𝑚𝑎𝑙
+ 𝐶𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛
= 1.4075
𝐼𝑠𝑝 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 =
(𝐶𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙
) (𝐶∗
)
𝑔0
= 273.5 𝑠𝑒𝑐𝑠
With our desired thrust = 10 lbf,
𝐹 = (𝐼𝑠𝑝 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙)(𝑚̇ )(𝑔0)
𝑚̇ = 0.03656
𝑙𝑏𝑚
𝑠𝑒𝑐𝑠
Geometry Discussion
Assuming the LH2/LOX system should also be able to undergo sea level testing where
P2 = 0.4*Pambient, the geometry can be the LH2/LOX system can be improved.
Since P2,Al and P2,Steel are both larger than the desired P2 = 5.88 psi, the expansion ratio would need to
be increased to allow the exit pressure of both the Aluminum and Steel desgin equal to the desired
exit pressure.
Other than the adjustment in expansion ratio, which would increase Isp performance, the reacting
gas seems like a viable option for the current cold gas geometry. Isp increased significantly and the
O/F were designed to allow the thrusters to thermally manage the heat loads.
21. Cold Gas Thruster Project
21
Aluminum Thruster Heat Transfer Analysis
Since the design temperature of the aluminum thruster was 800 Rankine, an O/F = 0.454 was used
to satisfy the constraint. The transport properties were determined by the CEA output and assumed
to be constant throughout the combustor length. In addition, the designed adiabatic wall
temperature is assumed to be 80% of chamber temperature.
With those conditions, the following values were determined:
Figure 12: Diagram of Temperature & Velocity Profiles Across Chamber Length
ℎ 𝑔 𝐴(𝑇𝑎𝑤 − 𝑇 𝑤,ℎ) =
𝑘𝐴
𝐿
(𝑇 𝑤,ℎ − 𝑇 𝑤,𝑐) Eqn. 20
𝑇𝑔 = 809.2 𝑅
𝑇𝑎𝑤 = 𝑇𝑔 𝑅𝐹; 𝑅𝐹 = 0.92 Eqn. 21
𝑇𝑎𝑤 = 744.46 𝑅
Using Bartz Equation to evaluate the heat transfer across the chamber wall,
ℎ 𝑔 = [
0.026
𝐷𝑡
0.2 (
𝜇0.2 𝐶 𝑝
𝑃𝑟0.6
)
𝑛𝑠
(
(𝑝 𝑐) 𝑛𝑠 𝑔
𝑐∗
)
0.8
(
𝐷𝑡
𝑅
)
0.1
] (
𝐴 𝑡
𝐴
)
0.9
𝜎 Eqn. 22
𝜎 =
1
[
1
2
𝑇 𝑤𝑔
(𝑇 𝑐) 𝑛𝑠
(1+
𝛾−1
2
𝑀2)+
1
2
]
0.68
[1+
𝛾−1
2
𝑀2]
0.12 Eqn. 23
Aluminum Chamber Thruster Properties
Dt 0.3007 in
μ
1.44E-
05
lbm/(in-
s)
Cp 0.5973
Btu/(lbm-
F)
(Pc)ns 100 psi
C* 5716 ft/s
R 0.2255 in
At 0.071 in^2
A 0.1867 in^2
22. Cold Gas Thruster Project
22
Twg 647.4 R
(Tc)ns 809.2 R
M 0
γ 1.392
Pr 0.6613
Table 14: Aluminum Chamber Properties
Calculations of the Bartz Equation can be examined in the Appendix section.
𝜎 = 1.004
ℎ 𝑔 = 0.0007448
𝐵𝑡𝑢
(𝑖𝑛2)(𝑠𝑒𝑐𝑠)(𝐹)
Examining aluminum, the thermal conductivity of Aluminum is 0.00317 Btu/(in-s-°F).
Since L=t=0.235 inchesand Tw,h = Taw, Tw,c can be calculated:
This gives:
Tw, c= 642 °R
Steel Thruster Heat Transfer Analysis
The same process repeated in order to perform a heat transfer analysis in the case of a thruster made
of stainless steel. Since the design temperature of the aluminum thruster was 1260 Rankine, an O/F
= 0.7075 was used to satisfy the constraint. The transport properties were determined by the CEA
output and assumed to be constant throughout the combustor length. In addition, the designed
adiabatic wall temperature is assumed to be 80% of chamber temperature.
Using Bartz Equation to evaluate the heat transfer across the chamber wall,
Steel Chamber Thruster Properties
Dt 0.3007 in
μ
1.68E-
05
lbm/(in-
s)
Cp 2.093
Btu/(lbm-
F)
(Pc)ns 100 psi
C* 6257 ft/s
R 0.2255 in
At 0.071 in^2
A 0.1867 in^2
Twg 1008 R
(Tc)ns 809.2 R
M 0
γ 1.38
Pr 0.6062
23. Cold Gas Thruster Project
23
Table 15: Steel Chamber Thruster Properties
𝜎 = 1.074
ℎ 𝑔 = 0.002822
𝐵𝑡𝑢
(𝑖𝑛2)(𝑠𝑒𝑐𝑠)(𝐹)
The thermal conductivity of Stainless Steel 309 is 0.000187 Btu/(in-s-°F)
Since L=t=0.235 inchesand Tw,h = Taw, Tw,c can be calculated:
This gives:
Tw,c= 469 °R
Heat Transfer Analysis Discussion
Comparing the aluminum and steel heat transfer analysis, it would be optimal to choose the steel
thruster design over the aluminum thruster design.
Even though the steel thruster is running at a chamber temperature higher than the aluminum
thruster, the outer wall temperature of the steel thruster was still lower than the outer wall
temperature of the aluminum thruster. This meant that the steel thruster could operate at a higher
chamber temperature and require less cooling than the aluminum thruster. Higher chamber
temperature would mean higher thruster performance while less cooling would mean a less
complex thruster design. Therefore the steel thruster design is in superior to the aluminum
thruster design.
As a Main Propulsion System
We considered whether or not the design that we came up with could be used as a main propulsion
system of a craft rather than just an attitude adjusting thruster.
Assuming the cold gas thruster has the same performance parameters previously calculated:
𝐼𝑠𝑝 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 = 61.284 𝑠𝑒𝑐𝑠
Assuming the test system has a mass ratio, 𝑀𝑅 = 0.05
The ideal rocket equation can be applied to calculate the amount of ∆𝑉can be expected from a
10,000 lbm cold gas thruster.
∆𝑉𝑐𝑜𝑙𝑑 𝑔𝑎𝑠 = −(𝐼𝑠𝑝 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙)(𝑔0) ln(𝑀𝑅) = 5912 𝑓𝑡/𝑠
Assuming this launch system wants to go to LEO, which requires a ∆𝑉 = 23000 𝑓𝑡/𝑠, this cold
gas launcher concept is not viable. The Isp of the cold gas launcher is simply too low.
24. Cold Gas Thruster Project
24
References:
1
Hedin, A. E., “MSISE Model 1990”, NASA Goddard Space Flight Center, 1990
2
Minzner, R. A., “The 1976 Standard Atmosphere Above 86km”, NASA SP-398, 1976
