Heating Analysis of Falcon Launch VII - Berger.pdf - United States ...

Heating Analysis of Falcon Launch VII
Andrea V. Berger 1 and Kenneth I. Bull 2
United States Air Force Academy, USAF Academy, Colorado, 80841
The FalconLAUNCH program at the Air Force Academy is in its seventh
year, designing the seventh rocket in the FalconLAUNCH series. This rocket is the
first two-stage rocket in the series including a boost phase and a non-boosted dart. It
is expected to go hypersonic, another first for the program. This speed introduces a
new thermal profile. This paper outlines the resulting thermal analysis of the dart
nose tip down through a portion of the body. This analysis was then used to estimate
temperatures through the rest of the body. The thermal approach used for
analyzing missile nose cones as outlined in the book Tactical Missile Design was
used as a basis to develop analytical tools for the program. It uses the flight profile
of the dart including its speed, altitude, and the corresponding free stream velocity
and temperature combined with the specific heat, thickness, and density of the
material used to calculate the skin temperature of the nose cone. The temperatures
past the nose tip are found using an iterative process where the distance from the
nose tip is varied. SolidWorks COSMOSFlow was used to find the steady state
conditions, and subsequently, a ratio between the steady state temperature and the
heat concentrations. This ratio was applied to the time variant model to estimate the
temperature at the heat concentrations. The ratio is a conservative estimate because
the ratio is calculated at steady state and during the flight regime, it will never reach
steady state conditions. The data calculated was validated by comparing it to a
similar flight profile.
Nomenclature
Ts = stagnation temperature
Tf = freestream temperature
r = recovery factor
MP = Mach number in the corresponding phase
Q = heat
ρf = freestream density
M = Mach number
d = distance from nose cone
Dt/dt = temperature change across wall
c = heat capacity
ρm = density of material
tw = thickness of wall
T = skin temperature
Ti = initial skin temperature
t = time at the speed and altitude
I. Introduction
FalconLAUNCH is a senior capstone project for undergraduate Astronautical Engineering majors at the United
States Air Force Academy (USAFA). The program allows undergraduates to design, build, analyze, test, and launch
1
Cadet, DFAS, P.O. Box 4388, Student.
2
Cadet, DFAS, P.O. Box 2739, Student.
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American Institute of Aeronautics and Astronautics

a rocket with a Department of Defense payload. It is made up of 23 senior cadets with 7 faculty mentors. This is the
seventh year in the program, each year a new rocket is produced and launched. The rocket design this year features a
two stage boosted dart design where the second stage is inert. The objective of the rocket is to reach space and
gather information on the effect of winglets on rocket fins going faster than Mach 4. It will be the first rocket in the
program with two stages. This created several interesting issues for analysis as the near-hypersonic environment
presents many heating and loading difficulties. Future rockets in the program are expected to go hypersonic, so an
analysis tool will be needed for a fully hypersonic flight profile as well. The program decided to attempt to create an
in-house thermal analysis tool. With a starting point in Tactical Missile Design and some conservative thermal
analysis provided by Alliant Techsystems, Inc. (ATK) and United Launch Alliance (ULA) as a method of
validation, a tool was created in Excel for this purpose. The mathematical basis behind the tool is explored in this
report.
II. Description of Tools
Several tools where used calculated and validate the thermal analysis of Falcon Launch VII
A. COSMOSflow
COSMOSflow is a computational fluid dynamics add-on provided by SolidWorks. It has the capabilities to
model high Mach number, as well as creating steady state and time dependent models. Models may be run using a
variety of initial conditions allowing for the ability to choose altitudes and speeds, different fluids besides air may
also be used. A problem that was encountered was COSMOSflow requires a large amount of computational
resources in order to be run properly. Time dependent models were impossible to run on our systems because it was
estimated to run for up to a month at the highest quality mesh setting. Another problem was the computer used did
not have sufficient memory to open the results of a high mesh model. The solution to these problems were to run
each simulation at steady state conditions with a lower quality mesh for a timely turnaround of three days. This
provided the most accurate model that did not use all of the computer’s resources, as well as providing a quick
results.
B. United Launch Alliance
United Launch Alliance (ULA) provided thermal analysis using MINIVER to perform an aero heating
assessment. They validated this assessment with FLUENT CFD simulation and used SINDA to performance a
detailed time phased thermal analysis to calculate the temperature distributions. Their simulations and analysis were
completed assuming constant Mach 5 flight and constant altitude for 300 seconds. The resulting data is extremely
conservative.
C. FalconLAUNCH VI Data
In 2007, AFRL provided thermal analysis for FalconLAUNCH VI. That rocket had a similar geometry with a
conical nose cone, and thermal data was provided for the nose tip up to Mach 5. So, this data can be used for
comparison and validation.
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D. Tactical Missile Design
Tactical Missile Design (TMD) 1 is a text written by Eugene L. Fleeman describing the design process for
missiles. It includes a section on how to predict the temperatures of the nose cone and body. The book also comes
with a CD, which has a spreadsheet that includes calculations for the maximum temperature. The TMD method
starts with calculations of a launch phase where a missile is fired from earth or a plane. Then, it has a boost phase
allowing the missile to reach the desired trajectory. Next it has a cruise phase where thrust is maintained to keep the
missile on its flight path, and finally it has a coast phase as the missile coasts in to detonate on its target. Each of
these phases is necessary for a missile, but the spreadsheet did not allow any phase to be turned off to meet rocket
needs, which are only launch for the purposes of the FalconLANCH VII rocket. Thus, this model was not accurate
enough to use by itself and was modified significantly to fit the needs of the rocket program.
III. Thermal Analysis Tool
A. Tactical Missile Design Beginnings
TMD is a missile design text, so in its thermal analysis section it focuses on launch, boost, cruise, and coast skin
temperatures of the nose cone and the body of the craft. On the rocket, only the launch and boost phases are needed.
This is particularly true for FalconLAUNCH VII because the rocket deconstructs at apogee deploying a recoverable
structure, so the temperature of the rocket structure no longer matters. As written, the spreadsheet provided on the
CD accompanying the text would not operate without information for all of the four phases. However, it provided
the core methodology and mathematics which lead to the development of the tool used for FalconLAUNCH VII.
B. Basic Mathematical Functions
The basic process is to find the stagnation temperature, then the heat, then the heat transfer at the wall, and
finally the skin temperature. This process requires flight profile information including the freestream temperature
and density, time, and Mach number at different times. It also required information about the material used. This
process is efficient, but ineffective as used in TMD because it finds these based on a short boost phase and long
glide phase at constant freestream density and speed. However, the equations as shown provided a basis to develop
a useful tool.
The stagnation temperature is found using the freestream temperature as shown in equation 1 1 .
2
Ts Tf
[ 1
. 2(
r)(
M P)
]
(eq. 1)
Ts: stagnation temperature
Tf: freestream temperature
r: recovery factor
MP: Mach number in the corresponding phase
The heat, Q, is dependent on the distance from the nose tip and freestream density as shown in equation 2 1 .
2.
8
M
0.
2
d (eq. 2)
Q: heat
ρf: freestream density
M: Mach number
d: distance from nose cone
0 . 8
Q 345(
f )
With the heat determined, the temperature change across the wall of the body can be found according to equation 3 1 .
c
Dt Q
dt
m w t
(eq. 3)
Dt/dt: temperature change across wall
c: heat capacity
ρm: density of material
tw: thickness of wall
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At this point, the skin temperature is found using equation 4 1 .
Qt
c
m ( Ts
Ti
)
s
T Ts
( Ti
T
)
(eq. 4)
T: skin temperature
Ti: initial skin temperature
t: time at the speed and altitude
Here, the spreadsheet and book end their contributions to the rocket thermal analysis as it takes a departure into the
realm of straight and level flight. However, the equations presented are vital to the tool developed for the rocket
needs.
C. Integration
A new spreadsheet was developed to fit the needs of the rocket program better. The program needed a tool to be
user friendly for students. It also needs to do calculations where Mach, time, and distance from the nose tip are
simultaneously variable. Excel was chosen as the most user-friendly interface, and a spreadsheet developed that does
the necessary calculations concurrently.
The first tab of the spreadsheet is definitions of variables used. The second is where the flight profile including
Mach number, speed, altitude, freestream density and freestream temperature are input for reference throughout the
workbook. This tab also houses the information about the material used including its specific heat, the wall
thickness, material density, and recovery factor. The third tab is a succinct output of results which will be described
later. The fourth tab begins the section of calculation tabs. It first finds the stagnation or recovery temperature using
equation 1. Next, it finds the heat using equation 2, followed by the change in temperature at the wall using equation
3, and finally the skin temperature using equation 4. The calculation tabs calculate the temperature at the desired
distance from the tip of the nose cone, with each subsequent tab finding the temperature some distance farther away
from the tip. Each individual tab calculates the temperatures with varying speeds matching the flight profile and
iterates to find the temperature as the Mach increases with the corresponding time increases as well. This creates a
way to track the changes in temperature as the rocket ascends as well as the changes in temperature down the body
tube simultaneously. Each calculation tab features a graph with altitude vs. Mach number and skin temperature vs.
Mach number for quick analysis. The results are summarized in the output tab, tab 3, where the maximum
temperatures found on each sheet and graphed against the distance from the nose tip for a full picture of the
temperature profile at the hottest time.
D. Output Data
The results show a maximum nose tip temperature of 1,664 o F with body temperatures decreasing from 357 o F to
134 o F with distance away from the tip as shown in table 1 and figure 1.
Table 1: Results
Distance from tip Maximum Temperature
ft ˚F
0.00000008 1664.601795
0.001 357.5283292
0.005 280.19313
0.01 253.512305
0.03 217.8667144
0.05 203.6990196
0.08 191.8475168
0.1 186.5889914
0.2 171.6402236
0.3 163.7896882
0.4 158.5857898
0.5 154.746693
0.6 151.7323487
0.7 144.8939403
0.8 142.9308945
0.9 141.2416654
1 139.7634311
1.1 138.4523711
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1.2 137.2767703
1.3 136.2129765
1.4 135.2429063
1.5 134.3524417
Figure 1: Output Chart
The maximum temperatures occurs around 5.5 seconds into the launch time exactly as predicted as this is the end of
the boosted phase of the rocket. The results led to important decisions on materials and coatings for the project.
The design impacts of this thermal analysis are summarized in section V.
IV. Validation
A. Comparison to COSMOSflow 4
Due to restrictions of our equipment, COSMOSflow could only be simulated as a steady state system. The
results from the COSMOSflow simulations were more extreme then FalconLAUNCH VII would experience in
flight. Because of this, COSMOSflow could not be relied on to give accurate data, but it could be used to identify
hot spots of the body of the rocket that the spreadsheet could not identify. For example, hot spots were discovered
on the interstage from where the shockwaves from the dart fins impacted the interstage. To estimate the hotspots, a
ratio was determined based on the highest temperature in the hot spot to the temperature surrounding the hot spot.
This ratio could then be applied to the temperatures calculated by the spreadsheet to determine the maximum
temperature that Falcon Launch VII would experience. The ratio at steady state is higher than the ratio would be
after a short period of time, but this allows for our estimates to remain conservative.
B. Comparison to United Launch Alliance
The data provided by ULA is a very conservative estimate of the thermal profile. It is not as detailed as the tool
developed at USAFA as it assumes constant freestream density and Mach number for 300 seconds. Because the 300
seconds are not correlated with changes in altitude or speed, the resulting data is very conservative. The ULA
method provided data showing the maximum body temperature of 1150 o F after 300 seconds, but is somewhere
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etween 200 o F and 300 o F after 5 seconds, the predicted maximum heating point 2 . The results are shown in figure 2.
These results validate the results found through the USAFA developed tool. The ULA results are summarized in
figure 2 2 .
Temperature, deg F
1400
1200
1000
800
600
400
200
FalconLaunch Temperature
with fin mount
0
0 50 100 150 200 250 300
Time, sec
Figure 2: ULA Results
C. Comparison to FalconLAUNCH VI
FalconLAUNCH VI data also validates the FalconLAUNCH VII tool. AFRL provided a thermal profile with a
maximum temperature of 1,940 o F at Mach 5.35 3 . This is slightly higher than the USAFA estimate, but is similar
enough to validate the resulting data is a good approximation of what can be expected.
V. Design Contributions
The thermal data gained from the analysis was integral in making several design decisions. The maximum
heating is expected in two areas according to the hot spots found in COSMOSflow: nose cone and interstage 4 . The
estimates for the temperature on the nose cone varied depending on the method, so Inconel 718 was chosen as the
nose cone material. This material maintained structural integrity past the AFRL estimate of 1,940 o F. This ensured
that even if the USAFA estimate is low, the rocket will not fail due to heating of the nose cone. The interstage was
coated with an ablative cork to keep the steel underneath from experiencing the extreme heating. This measure
ensured the program did not trade structural integrity for thermal properties. Other coatings were considered for the
body tube so that a more available material could be used, but ultimately the thermal analysis proved the steel
chosen would be successful in the heating environment. While there are not temperature stain gauges on the rocket,
the hardware can be recovered to validate the materials chosen were effective and the estimates were correct. It has
been proposed that the next rocket in the program be wired to record the actual thermal data from flight to further
validate the model.
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Dart Body
Dart Fin
Fin Tab
Booster Fin

VI. Conclusion
The thermal analysis tool developed for in-house thermal calculations for the USAFA FalconLAUNCH program
is accurate based on comparison validation for the nose tip through the body. Design decisions made based on the
results of the analysis were integral to the program. Having this tool has made a significant impact on the ability of
the program to make informed decisions and move forward to launch with confidence. Further, with this tool in
hand, FalconLAUNCH VIII can improve their rocket design and ultimately do thermal tests on launch to further
validate the tool. Testing will be more credible proof of the tool’s accuracy. While this tool alone provides thermal
analysis for the components of the rocket most susceptible to thermal failure, it also sets up for the future when
cadets expand upon the spreadsheet by adding thermal analysis for fins and other parts of the rocket. It can also be
combined with another tool currently in house which calculates the temperature on the inside of the body tube based
on heating on the outside. These tools together would provide an all-in-one comprehensive thermal analysis. This
tool has laid the groundwork for future endeavors into a previously impossible task for the program.
Acknowledgments
Thanks to United Launch Alliances for providing us with a comprehensive CFD analysis of FalconLAUNCH
VII.
Thanks to Air Force Research lab for providing CRD analysis to FalconLAUNCH VI which was integral to this
year’s endeavors.
References
1 Fleeman, Eugene L. Tactical Missile Design. 2nd ed. Reston, VA: AIAA, 2006. Pages 162-170.
2 Chern, S. FalconLAUNCH VII Thermal Analysis. Tech. ULA, 2009.
3 FalconLAUNCH VI Thermal Analysis. Tech. AFRL, 2007.
4 SolidWorks COSMOSflow, SolidWorks Academic Edition 2008 SP4.0.
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