NASA Technical Reports Server (NTRS) 20030065626: A Thermal Analysis Approach for the Mars Odyssey Spacecraft's Solar Array

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S
AIAA 2003-3764
A Thermal Analysis Approach for the Mars
Odyssey Spacecraft's Solar Array
John A. Dec and Ruth M. Amundsen
NASA Langley Research Center
Hampton, VA
36th AIAA Thermophysics Conference
23-26 June 2003
Orlando, Florida
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A THERMAL ANALYSIS APPROACH FOR THE MARS ODYSSEY SPACECRAFT’S
SOLAR ARRAY
John A. Dec and Ruth M. Amundsen
National Aeronautics and Space Administration
Langley Research Center
Hampton, VA 23681-2199
ABSTRACT axis stabilized spacecraft to perform this type of
multipass aerobraking1. Mars Global Surveyor, the
There are numerous challenges associated with placing second to use multipass aerobraking, gradually reduced
a spacecraft in orbit around Mars. Often, trades must its orbit from an elliptic 45-hour period to about a
be made such as the mass of the payload and the 380km 2-hour circular orbit.
amount of fuel that can be carried. One technique
employed to more efficiently place a spacecraft in orbit To control periapsis altitude, Magellan planned on
while maximizing payload mass (minimizing fuel use) using thermocouple data to signal the need to perform a
is aerobraking. The Mars Odyssey Spacecraft made use periapsis raise maneuver, which would raise the
of aerobraking to gradually reduce its orbit period from periapsis altitude, lower the maximum atmospheric
a highly elliptical insertion orbit to its final science density experienced, and thus lower the aerodynamic
orbit. Aerobraking introduces its own unique heating on the spacecraft and solar arrays. In the
challenges, in particular, predicting the thermal literature, it was noted that Magellan experienced at
response of the spacecraft and its components during least 5 thermal sensor failures prior to the start of
each aerobraking drag pass. This paper describes the aerobraking2. It is unclear from the available literature
methods used to perform aerobraking thermal analysis if any of these thermal sensors were located on the solar
using finite element thermal models of the Mars arrays and were to be used during operations. It is also
Odyssey Spacecraft’s solar array. To accurately model unclear whether or not there were any thermal models
the complex behavior during aerobraking, the thermal developed and used during the Magellan aerobraking
analysis must be tightly coupled to the spatially process to make up for the inoperable thermal sensors,
varying, time dependent aerodynamic heating analysis. but there are references to heat rate and surface
Also, to properly represent the temperatures prior to the temperature calculations being performed using a direct
start of the drag pass, the model must include the orbital simulation Monte Carlo particle method3,4. In any
solar and planetary heat fluxes. It is critical that the event it is clear that in the early 1990’s the limitations
thermal behavior be predicted accurately to maintain of computers would have prohibited the use of a
the solar array below its structural flight allowable sufficiently detailed finite element or finite difference
temperature limit. The goal of this paper is to describe model that could have been run in a timely enough
a thermal modeling method that was developed for this fashion to be used during operations. During the Mars
purpose. Global Surveyor operations, the heat rate encountered
during previous drag passes was reconstructed using a
INTRODUCTION 1-dimensional thermal model at various locations
around the solar arrays. This model used the spacecraft
and solar array thermal sensor temperature data as input
The Mars Odyssey spacecraft was launched on a Delta
to determine what heat rate the spacecraft and solar
II launch vehicle from Cape Canaveral Air Force
Station on April 7th 2001. On October 23rd 2001, after a arrays experienced. A thermal model to predict the
solar array temperatures for future drag passes and to
197-day cruise, the spacecraft performed a propulsive
reconstruct the solar panel temperatures for past orbits
maneuver to insert itself into an 18.5-hour elliptic orbit
was not available. Originally, during operations, the
around Mars. To place itself into its 2-hour, 400km
plan for Mars Odyssey was to use a 1-dimensional
circular, sun-synchronous mapping orbit, Odyssey used
thermal model similar to that of the Mars Global
the multipass aerobraking technique, the same
Surveyor model. Unlike Magellan and Mars Global
technique utilized by the Magellan spacecraft around
Surveyor, Mars Odyssey was the first multipass
Venus and the Mars Global Surveyor spacecraft around
aerobraking mission to make use of detailed 3-
Mars. Aerobraking makes use of atmospheric drag on
dimensional finite element thermal model during
each orbit pass to gradually reduce a spacecraft’s
operations to predict the temperatures for future orbits
velocity at periapsis, which then reduces the altitude at
and reconstruct the solar panel temperatures for past
apoapsis. The Magellan spacecraft was the first three-
orbits. This model, used in addition to the 1- while the mid panelhas a unique geometry. Figure 1
dimensional model, provideddetailed,3-dimensional showsa 3-dimensional geometricrepresentation ofthe
temperature profilesof the solar array, transient plotsof solar array. This geometric representation was
maximummaterial temperatures, and transient plotsof developed inMSC/PATRAN and wasused in the
thermal sensor temperatures. It alsoprovided the aerobraking thermal analysis. Eachpanel consists of
ability to identify thehottest spots on the solar array, five layers; the first three make up the structural
and provided a means to develop thermal limits based components andprovide the structural integrity during
onheat rate or atmospheric density. launch and throughout aerobraking. Specifically, the
solar array structure is a sandwich construction with a
THERMAL MODEL DEVELOPMENT 0.190mm (0.0075”)facesheet of M55J/RS-3 graphite
composite, a 19.05mm (0.75”)5052 aluminum
honeycomb core, and another 0.190mm (.0075”)
The thermal analysis of the solar array had three main
M55J/RS-3 composite facesheet.
components: the view factorand orbital heating
analysis, the aerodynamic heating analysis, and the
computationof solar array temperatures. The
calculations were performedintwo flight regimes. One
regime was the vacuum phase where the spacecraftwas
in orbit around Mars,butoutof the atmosphere. The
thermalenvironmentinthis phase was dominated by
the solar and planetaryheating withnegligible
aerodynamic heating. The secondregime was the
aerobraking phase, or drag pass,where the spacecraft
made its excursion into the atmosphere. The thermal
environment in thisphase was dominated bythe
aerodynamic heating (roughly60 times greater than the
orbital heating). Temperatures were calculatedforboth
flightregimes. Accurate calculationof the
Figure 1. 3-D geometric representation of the Mars
solar/planetary fluxduring flight,as well as
Odyssey solar array.
aerodynamicheating during drag passes,requires that
the thermal analysis be tightly coupled to the flight Thenext layeris a 0.051mm (0.002”)Kapton sheet that
mechanics, aerodynamics, and atmosphericanalysis. is co-cured to the M55J/RS-3graphite beneath it. The
next layer is the solar cell layer and is made up of
Solar ArrayDescription severalsublayers: 0.190mm (0.0075”)Gallium
Arsenide solarcells, 0.152mm (0.006”) cover glass, and
The function ofMarsOdyssey’s solar array is two-fold. 0.229mm (0.009”) of adhesives6. Figure2 shows a
First, its primary function is toprovide a stable power cross-sectional view of the solar array at a
sourcefor the spacecraft andscientific instruments representative location.
during all phases of the mission. Second,while in the
stowed configuration, the solar arrayprovides a large
surface areaon which the aerodynamic forces can act
during eachdragpassof aerobraking. Following Mars
orbit insertionthe Odyssey spacecraftbegins
aerobrakingby slicing through the Martian atmosphere
at a relativevelocity of about4.57 km/s. Despite low
atmosphericdensities of about 80kg/km3, these high
velocities, along with thelarge exposed surface area,
produce significant aerodynamic heatingon the solar
array, and spacecraft. Careful design and construction
of the solar array allows it to withstand this
aerodynamic heating.6
Figure 2.Cross-section of Mars Odysseysolar array
The Mars Odyssey solar array is a three panel, layered Toreinforce certain areasof the array,sectionsof the
constructionof low density materials. Thepanels are standard 19.05mm (0.75”) thick,1.0 lb/ft3 aluminum
commonly referred to as the +X,-X, and mid panels. honeycombcore were replaced with a higherdensity
The +X and–Xpanels are mirror images of each other, core of the same thickness. Also, to reinforce the
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array’shard points,a doubler sandwichstructure was On the engineeringdrawings6, the thermal sensors are
used. Thedoubler sandwichstructure consistedof designated T1,T2, T3, T4, and T5. T1 andT4 areon
0.381mm (0.015”) layersof M55J/RS-3graphite the +/-X panelon the exposed facesheet side. T2, T3,
composite on either side of a18.161mm (0.7125”) and T5 are on the solar cell side; Figure1 from above
aluminum honeycomb core. Thedoubler core densities shows the locationsof the thermal sensors on the solar
varieddepending on the locationwithin thearray and array.
the expected loading in the regionof concern.
Examples of such reinforced hard points on thearray Orbital Heating Modeling
are the hingemountingpoints. Overall, thearray
designmakes use offour different densityaluminum Theorbital heating and viewfactor analysis,or
honeycomb cores. Figure3graphically displays the radiation model, was performedusing Thermal
locations of the different cores used and Table 1 lists Desktop, a commercially available software package.7
the density and thicknessof aluminum coreusedwith The radiation modelwas developed usingengineering
respect to the colors in Figure 3. The table entries drawingsof the spacecraft and solar array.6 View
where the corethicknessdeviates from the nominal factor and heat rate calculationswere performed for
0.75” thickness also show the locationsof the M55J severaldifferent solar array configurations and
doublers. Thedoubler thickness is such that it brings spacecraftorientations. First, calculations were made
the sectionback to thenominal panel thickness. with the spacecraft and solararray in its vacuum phase
configuration; the spacecraft orientedwith its high gain
antennapointed towards Earth and thesolararray
normal to the sun. In transitioning to theaerobrake
configuration, both heat ratesand viewfactors to space
for the solar array were calculated as the solar array
articulated to its stowed position.As the spacecraft
slewed to the aerobraking configuration, thesolar
array’s viewfactors to spacedidnot change, so view
factors did not haveto be recalculatedforthat
maneuver.
Figures4 and5 show the spacecraft and solar array in
Figure3. Variation in aluminum honeycomb core the aerobrake configurationandvacuum phase
density (lb/ft3) respectively. Thispartof the analysis requireddetailed
knowledge of the orbit andspacecraft orientation,and
Table 1. 5056 Aluminumhoneycombcore thus was highly dependenton theflight mechanics
analysis. Theorbital elements in thevacuum phase
Marker Density(lb/ft3) Thickness(in)
were obtainedfrom a mission trajectoryrun-out
Red 1.0 0.75 performed by JPL8. For thedrag passphase, theorbital
Yellow 2.0 0.75 elements wereobtainedfrom POST simulations and
Green 3.1 0.715 outputin unit vector form.
Blue 12.0 0.715
Toprotect thearrayfrom aerodynamic heating, a
0.072mm (0.00283”) thick layer of multilayer
insulation (MLI)wasplacedon the facesheet exposed
to the aerodynamic heating and around theedgesof the
M55J/RS-3 graphitefacesheet. Thebulkof the MLI
wason the facesheet surface,and a small portion
wrapped around the edges and terminated on the solar
cell side. Thewidth of the MLIon thesolarcell side
ranged from 50 –148mm (1.96-5.83”).
Velocity Vector
The solar array has five thermal sensors. There isone
sensoron themid panelon the solar cell sideof the
Figure 4. Mars Odyssey Thermal Desktop model in
array. The +X and –Xpanels each haveone sensoron
the aerobrakeconfiguration.
the solar cell side and one on the “hot”facesheet side.
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Againwith the spacecraftremovedfor clarity, Figure 7
shows a representative resultof the solar/planetary
heating nearperiapsis.
Figure 5. Mars Odyssey Thermal Desktop model in
thevacuum phase configuration, view from Earth.
Thevacuum phaseorbital elements were input into Figure7. Typical orbitalheat flux nearperiapsison
Thermal Desktop via the “Keplerian Orbit” input the facesheet exposed to aerodynamic heating in the
option. Thisorbital inputform requires theperiapsis aerobraking configuration.(W/m2)
altitude,orbit eccentricity, right ascensionof the sun,
After completing theorbital heating and view factor
right ascension of the ascending node, and the argument
calculations, this datahad tobe input into PATRAN
of perigee. The vectoroutput from POST is input into
Thermal for use in the temperature calculations. This
Thermal Desktop byusingthe “Vector List” orbit
process will be explained in detail later in the boundary
optionwhere theuser supplies the time, the unitx, y,
conditions anddata exchangesection.
and z componentsof thevector from the probe to the
sun, and the unit x, y, and z componentsof the vector
Aerodynamic Heating Analysis
from the probe to the planet. Theuser also supplies the
ratioof thedistance to thespacecraftfrom the planet
center and theplanetradius. With the spacecraft The aerodynamic heating analysis consistedof
calculating theatmosphericdensity, the spacecraft
removed forclarity,Figure 6 showsthe viewfactors
calculatedwith the solar array in the stowed,or velocity relative to the atmosphere, and theheating
aerobraking configuration. The view factorsshownare coefficient for points spatially across the array. Using
this information, the incident aerodynamicheating was
for the facesheet exposed to the aerodynamic heating;
the solar cell sidehas anunobstructed view to space so calculated usingequation 1,
the viewfactor is equal to 1.0. Notice that the
spacecraftprevents most of the middle panel from 1
Q (cid:32) (cid:152)(cid:85)(cid:152)V3 (cid:152)C (1)
seeing deep space (low viewfactor); fortunately, the i 2 H
spacecraft also shields the middlepanel fromthe
aerodynamic heating thus,preventing a potential
where(cid:85)(cid:3)is theatmosphericdensity, V is therelative
thermal problem due to inadequateradiative cooling.
velocity, and C is the heat transfer coefficient. This
H
calculationwas made at 5-second intervals throughout
the aerobrakingpass togivea transient representation
of aerodynamic heating. A databaseof theheat transfer
coefficientswas developedusing a Direct Simulation
Monte Carlo(DSMC)particle method -- specifically
the programs DAC andDAC free wereused. From the
POST simulations, the flightmechanics team was able
to provide theatmosphericdensity and the relative
velocity as a function of time(during operations, to
reconstructpast orbits, the density was calculated using
acceleration readings fromthe flight accelerometer)9.
Using thedensity and the relative atmospheric velocity,
Figure6. View factors to spacefor the facesheet
the heating coefficientswere calculated. Due tothe
exposed to aerodynamicheating in the aerobraking
longrun timesneeded toperform the DSMC
configuration.
computations,an aerothermodynamic database was
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developedprior to aerobraking. Then for each time coverglass, wire, solder, andadhesives thatwere
step, thedensity was calculatedby interpolating on modeled as anaveraged mass spread evenly across the
either the accelerometer data, or the calculateddensity layer. Thiswas an engineering approximation since the
versus time outputfrom POST. Forboth cases, the wire, solder, etc.,were not evenly distributed across the
heating coefficients across the array were calculatedby panels. The titanium hinges and dampers that
interpolating betweendensity andrelative velocity. physically connect the three solarpanels were also
The interpolation error on the heating coefficients was included in the model and provided a thermal link
calculated to be about2%,whichwas within the between the threepanels. The model was highly
accuracyof the DSMC calculations. Theheat transfer detailed and included the variations in the aluminum
coefficients ranged fromapeak value of 0.90 toalow honeycomb coredensity as well as thevarying
value of 0, andincluded the surface accommodation thicknessof M55J composite facesheet doublers. For
coefficient. allmaterials, propertieswereincluded as functionsof
temperature;for the aluminum honeycomb core and
Reflectedheatis a phenomenon which occurswhen M55J facesheets, orthotropicmaterial properties were
particles striking thesurfaceof the solar array leave the included. Thefive spacecraftthermal sensors were
surfacewith more energy. This occurs when the modeled as bar elements whichhad mass and were
surface temperatureof the solar array has increased thermally connected to the spacecraftwith acontact
enough to impart some of its thermal energy to incident resistance. Overall, the PATRAN thermal model was a
particles which are at a lower energy level. The physically accurate 3D representation of the solar array.
thermal modelaccountsforreflected heat, which was Compared to the as-built mass of the solar array of 32.3
approximated empirically for this mission using kg, the mass of the PATRANthermalmodel was 33.4
equation2 andis a functionof the incident heat flux kg, a difference ofonly3.4%.
and surface temperature.
The PATRAN thermalmodelrequiredinput boundary
conditions fromthe two analysis components
(cid:170) (cid:167) Q (cid:183)(cid:186) (cid:167)T (cid:183)
Q (cid:32)1(cid:85)V3(cid:171)0.015(cid:14)0.1(cid:168)1(cid:16) i (cid:184)(cid:187)(cid:152)(cid:168) wall(cid:184) (2) mentioned earlier. The model included radiation to
ref 2 (cid:171)(cid:172) (cid:168)(cid:169) 12(cid:85)V3(cid:184)(cid:185)(cid:187)(cid:188) (cid:169)300(cid:185) space, incorporating the view factors that were
calculated from Thermal Desktop. Theorbital and
planetary heat fluxes calculatedfrom Thermal Desktop
where T is the surface temperatureof thesolar array.
wall were applied to the surfacesof the model as well. The
Equations 1 and2reveal the couplingof the thermal
aerodynamic heating and reflected heating boundary
analysis to the flight mechanics, aerodynamics and
conditionswere applied tothe exposed M55J facesheet
atmospheric analysis. These calculationsprovided an
and MLI surfaces. Heatingon the edges of thepanels
accurate representation of theaerodynamic heating as
was included as 5% of the incidentheatingof the nodes
well as reflectedheating thatwas a functionof time as
closest to the edge. Edgeradiationwas included around
wellas position onthe solararray.
the outer-most edgeswith a view factor to space of 1.0.
Radiationback to the spacecraft bus was included,with
Temperature Calculations
the spacecraftbus simplymodeled as a node with a
constant temperature.
The temperatures for the solar array were calculated
with the commercially available software
Boundary Conditions andData Exchange
MSC/PATRAN Thermal10. Like the Thermal Desktop
model, a 3-Dmodel of the solar arraywasdeveloped
The processof applying the aerodynamic heat loads,
solely using engineeringdrawings6. Normally, it is less
orbital heat loads,and integrating theviewfactorsfrom
efficient to create two thermalmodels,however, since
Thermal Desktop into PATRAN was developedfor
existing FORTRAN codewould allow simple inclusion Mars Global Surveyor11. These processeshad to be
of the aeroheatingfluxes in PATRAN andbecause
modified slightly to accommodate the MarsOdysseys
existing methods couldbe easily applied11, this
solar array configuration andsimplified slightly to be of
inefficiency was nullified. Also, the Thermal Desktop
use during Odysseys’operationsphase.
radiation model was necessary sinceorbital heating
capabilities donot existwithin MSC/PATRAN.
The processof applying the aerothermodynamic heat
loads calculated by DAC to the PATRAN thermal
ThePATRANmodel represented all three solarpanels,
model involved the useof aMATLAB script and
and includedbothfacesheet layers, the aluminum
customized FORTRAN program that interfacedwith
honeycomb core, theKapton, the MLI, andone layer
the PATRAN solver at runtime. Incorporating the
for the solar cells. The solar cell layer included the
view factorsand orbital/planetary heat loadscalculated
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by Thermal Desktopdid not require the useof the the solution converges, the solver moves to thenext
customized FORTRAN codeor the MATLAB script, time step and the process is repeated. Figure 8 shows
but didrequire several preprocessingstepsin orderto the DSMC data mapped to the PATRAN modelwith
import the data intoPATRAN. The MSC/PATRAN the final resultof equation1plotted.
Thermal user’s guide10 describes howtoincorporate
user suppliedFORTRAN subroutines, and therefore it
willnot be discussed here. However,the processand
flowofdatafrom the aerothermodynamic database to
the PATRAN thermalmodel will bedescribed. As
mentionedpreviously, an aerothermodynamic database
wasdeveloped prior to the start of Odyssey’s
aerobraking. Thisdatabase consistedof a spatialmap
of the heat transfer coefficients over the array as a
Figure8. Example of aerodynamic heating mapped
function of atmospheric densityand relativevelocity. to the PATRAN model(W/cm2).
The drag pass duration, which definedthelength ofthe
transient in the thermalmodel, was providedby the
flight mechanics team. Alongwith the drag pass Theprocess for importing Thermal Desktopdata into
duration, theyprovided a time history of the PATRAN Thermal is not straightforward and is labor
atmosphericdensity and relativevelocity, the time intensive. First, a nodal positionreport must be created
interval ofwhich was five seconds. Priorto the from within PATRAN. This report isnothing more
executionof the PATRAN thermal analysis, the than a textfile that contains the node number, X,Y, and
MATLAB script was executed. The MATLAB script Z locationsof thenodes. Thenodes selectedfor
read thedensity, andrelativevelocity data, as well as inclusion in this report are associatedwith the surfaces
the aerothermodynamic database, and for each time in the thermal model that have theradiationboundary
intervalperformed an interpolation overdensity and condition imposedon them. Since thephysical location
relative velocity to obtain thespatial heating of the solar array withrespect to the coordinate system
distribution. The MATLAB script’s outputwas a file is different in the PATRAN and Thermal Desktop
that containedblocksof datawith the time interval as a models, some corrections to thenodal coordinates had
heading for eachblock, and a table ofX, Y,and Q, to be made. These corrections were made in Microsoft
whereX andY are the spatial coordinates ofthe DSMC Excel and saved as a new text file. Thedisconnect in
grid and Q is the incident heat flux calculatedby the physical locationof thearray was due tothe fact
equation 1. Uponexecution ofthe PATRANthermal that the spacecraftbuswas modeled in Thermal
analysis, thePATRAN solver makes a call to the Desktop,but was not modeled in PATRAN. In
customized FORTRAN subroutine. The subroutine Thermal Desktop, the originwas the centerof the
performs an initializationby reading the MATLAB spacecraft, and in PATRAN, theoriginwas along the
outputfile andstoring thedata in a three dimensional bottom edgeof the array at the midpointof the middle
array. The first two indices for the array are the number panel. Once the correctednodal position report is
ofX and Y points onthe DSMC grid. The thirdindex acquired, the Thermal Desktop model is runto solvefor
is a time indexwith its maximum value equal to the the viewfactors to space and theorbital heat rates.
numberof output time points provided in the Utilizing the internal interpolationroutine inThermal
density/relative velocitydata. With this initialization Desktop called “map data to locations”, thePATRAN
procedure complete the FORTRAN subroutine passes nodalpositionreport is supplied as input and Thermal
back control to the PATRANThermal solver, where it Desktopproduces a textfile that includes the PATRAN
begins its iterative solutionprocess. For every time nodenumber and the mappedThermal Desktop data.
step in the solution and at every node location thatwas Thisfile then needs tobe imported into PATRAN as a
flagged as having incident aerodynamic heating, the spatial field. This is accomplishedby using the
PATRAN solver makes a call to the FORTRAN spreadsheetutility in PATRAN. To import thedata,
subroutine. The subroutine thenperforms two simply start the spreadsheetutility in PATRAN, then
interpolations. The first is an interpolation over time to using standardwindowsfile open procedures, open the
obtain the heating at the correct time in the trajectory. ThermalDesktopdata file. The opening procedure
The second interpolation is over X andY to obtain the loads thedata into the spreadsheet, thenan internal
heating for thecurrentnode,sincethe x and y locations PATRAN spreadsheet functionisused to create a field
for the PATRAN nodesdiffer from the DSMC grid from the spreadsheet data. Thefieldgenerated is a
node locations. The FORTRAN codepasses thenodal finite element field and canbe used as the inputfor the
heat rate back to the PATRAN solver and the solution “FormFactor” entryinthe gap radiation boundary
process continuesuntil convergence is obtained. Once condition dialogbox. All of theradiationboundary
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conditions to space were created in thisway. Figure 9a determine the temperatures,where the aerodynamic
shows the view factors to space in the Thermal Desktop heating wasdominant. Temperature predictions were
model and Figure 9b shows theviewfactors as mapped made prior to eachdragpass and temperatures were
to thePATRAN model. Asimilar procedure is calculatedusing actual spacecraft telemetry to
followed to import the heatrate data from Thermal reconstruct pastorbits.
Desktop to PATRAN. Thisprocedurebecomes
cumbersome if theheat rates varygreatly over anorbit, TEMPERATURE PREDICTIONS
or if the viewfactors change,as is the casewhen the
spacecraft slews and stows the solar array prior to a
The initial goal of the thermal analysis was to provide
dragpass. To include these changes, the transientprior
an independent validation and verification of the
to thestartof thedragpass had to be brokeninto stages.
analysis already beingperformed on the solar array.
Each stagewas solved independently and each
This includedverifying the location and magnitudeof
successive stage used theprevious stage’sfinal
predictedhot spots on the array, andverifying thesolar
temperatures as its starting temperature. The only
array’s thermal limit. Thethermal limit is expressed in
exceptionwasthe first stagewhere the steady state
terms of theheat flux level and is that heatflux which
temperatures were calculated for the solar array in the
would cause the solar array to exceed its flight
vacuum phaseprior to the start of the slewing and
allowable temperature of 175°C. Thehighfidelity
stowing operations. The temperatures calculated by the
natureof this3-dimensional analysis, and the speed at
final stage before thedragpass beganwereused as the
which analysis results could be produced,were
initial solar array temperatures for the start of the drag
compelling evidence to include this analysis in the
pass.
trajectorydecision making process during aerobraking
operations. However, inorder for the analysis tobe
usefulduringoperations, temperatures needed to be
calculatedand postprocessed within 4 hours.
Utilizing a 1.7GHz dualXEON processorcomputer
made it possible for thishighly detailed finite element
analysis torunin about onehour. Although, as drag
passduration increases, sodoes therun time. This
increasewas slight, andfor the longest dragpasses the
solution time never exceeded1hour15 minutes.
Computer speed alone was not the only meansof
(a) increasing efficiency. The spacecraft’sconfiguration
in thevacuum phasewas always the same so vacuum
phase temperatures remainedvirtually constant. Also,
the occultation duration changed very slowly, causing
the initial temperatures to change at a slow,predictable
rate. Therefore, to increase analysis efficiency, the
viewfactor,orbital heating, and vacuum phase
temperature analyses couldbe performed onan as-
neededbasis.
(b)
Figure9. View factors to space: (a) Thermal
The thermal analysis was highly dependenton all of the
Desktop, (b) mapped toPATRAN
otheranalyses being performed. Any problemsarising
within anothergroup’s analysis causeddelays in the
The temperatures obtainedprior to thedragpass were
completion of the thermal analysis. Thishighly
primarily dependenton theorbital heat ratesand view
detailed thermalmodel generated a largequantity of
factors calculatedfrom Thermal Desktop,but most
information about the thermalstate of the solar array.
significantly, they were influenced by thefact that the
Figure10 shows the predicted temperaturedistribution
spacecraftpassed into solaroccultation andwas shaded
for orbitpass 40, justafter periapsis,which is typical of
by Marson average, for about 4 minutes before the
the majority of thedragpasses encountered. This
dragpass began. This reduced the initial temperatures
temperaturedistribution was calculated usinga
and allowed the solar array to absorb more energy and
predicteddensity, and velocity profile, and assumed a
therefore increased the marginbetween the flight
nominal orientationrelative to the atmosphere. Figure
temperatures and the thermal limits. Finally, during the
11 shows thepredicted temperature of the thermal
dragpass, a transient analysiswasperformed to
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sensors and the predicted heat rate as a function of time phaseof aerobraking, the magnitudeof the temperature
centered onperiapsis. differencebetween the materialmaximum and the
thermalsensor maximumwas dependent onthe heat
flux, and the difference grewas the magnitudeof the
heat flux grew.
70 0.25
60 Maximum facesheet
Maximum core 0.20
50 Maximum solar cells
C)40 1/2 RhoV3 2m)
Temperature (°2300 00..110531/2 Rho*V (W/c
10
0.05
0
Figure 10. Predicted temperaturedistributionon -10 0.00
-250 -200 -150 -100 -50 0 50 100 150 200 250
the solar arrayfor orbit pass 40. Time (s)
Figure12. Maximum predicted material
A similar transient plotwas generated for each material, temperatures, orbit pass040,peak heat flux = 0.232
where the maximum predicted temperature for any W/cm2.
locationon thatmaterial is tracked. Figure12 shows the
In all of the trajectories thatwere encountered, the
maximummaterial temperatures as a function of time.
materialmaximum was always higher thanwhat the
0 0.25 thermal sensors indicated and was always located in the
lower, outboard quadrant ofthe+X panel. Another
-10
minordifference between the thermal sensor and
0.20
-20 maximummaterial temperatureplots is due to the fact
that the locationof the maximum materialtemperature
C)-30 2m
Temperature (°--5400 00..110531/2 Rho V W/c ctsheheearmneg sse etdoe mtjhu rmtooupbg, eht hodeui stmc tohanxetiidmnruuaigmtipe tsae smasn.p d eI rntahtFeu itrgeeum srehp ie1frt2as twtuorheere
another node in thatparticular material layer.
-60
0.05
T1 facesheet side -X T2 solar cell side-X In Figures11 and 12, theheatrate is represented by a
-70 T3 solar cell side mid T4 facesheet side +X
T5 solar cell side +X 1/2 rho V3 smooth gaussian likeprofile. Theheating is directly
-80 0.00 proportional to the atmospheric density; the density
-250 -200 -150 -100 -50 0 50 100 150 200 250
Time (s) predictions,which came from an Odysseyversion of
Mars GRAM2000, donot accountfor atmospheric
Figure 11. Thermalsensortemperature predictions,
density variations and thushave an average density
orbitpass 040,peak heat flux= 0.232W/cm2.
profile as a functionof altitude. Large uncertainties in
Thisplotdiffers slightly from the plot of the thermal predicting theatmosphericdensity from orbit to orbit
sensor temperatures. Theobvious difference is that the made the temperature predictions less valuable than
maximum materialtemperatures are significantly expected,but they were still useful in that they gave a
higher than the predicted thermal sensor temperatures. 3-dimensionalpicture of the thermal state of the array,
In the case of the M55J graphite, whichwasexposed to and could identify any thermal anomalies.
the flow, the figures show that the peak temperature Although theuncertainties inthe density predictions
was85°Chigher than thepeakon either of the were present, they didnot impact thepredictionof the
facesheet thermal sensors, T1 and T4. This was a result thermal limit lines, which turnedout tobe a very useful
of having MLIcovering the facesheet in the areasnear tool. The flight corridor formain phase aerobraking
those thermal sensors. The MLIprovided sufficient was chosen basedon the maximum Q dot,whichwas
shielding to the underlying material from the incident the valueof the aerodynamicheating that would cause
heat flux toprevent the material in thoseregions from the solar array to exceed its flight allowable
reaching higher temperatures. Throughout the main temperature limit for the structureof 175°C. Theupper
7
American Institute of Aeronautics andAstronautics
flight corridorwasreducedby a factorof 2 to carry of the solar array. The Lockheed limit line was more
100% marginwithrespect tothe limit. Figure13 is a conservative and as suchwas used as the flight
plotof the maximum solar array temperature as a maximum.
function of Q dot,covering orbitpasses 77through99.
This plot was generated byrunningthe PATRAN 0.90
thermalmodelwith varying densityand henceheating
0.80
profiles. Fourdifferent density profileswere used: the
low, middle, and upper ends of the flight corridor, as 0.70 LaRC Qdot limit for 190°C
LaRC Qdot limit for 175°C
well as one that would produce a maximumQdotof 2m)0.60
0.8 W/cm2. A Q dot of 0.8 W/cm2 was chosen as the W/c
upperbounding case becauseit guaranteed the solar mit (0.50
atermrapyepraretudriectoiofn 1w75o°uCld. eBxyc euesdin tghea fplrigedhitc atleldo wQa dbolet,or Heatflux li00..3400
one derivedfrom flight data, the JPLNavigation team
0.20
could quickly determinethe maximumpredicted
temperature of the solar array. Determining the thermal 0.10
limit of the solar array in terms of theQdot was 0.00
0 5000 10000 15000 20000 25000 30000
obtainedsimply by finding the value ofQdot that
Apoapsis Altitude (km)
corresponded to 175°C. Figure13 is a snapshot of
temperature vs, Qdot over a small interval. This same Figure 14. Thermallimitline encompassing the
processcould be repeated for several orbit trajectories, entire mission.
and a mission thermal limit line couldbegenerated.
Figure14 shows the limit line as determinedby the
CONCLUSIONS
PATRAN thermalmodel plotted as a functionof
apoapsis altitude. The two limit lines show how
significant theallowable temperature is in determining It has beenshown that a 3-dimensionalfinite element
the thermal limit of the array. Simply increasing the model developed to representthe actualflight hardware
flight allowable temperature to190°C will increase the of the Mars Odyssey solar array canbeusedwithout a
thermal limit by about10%.As the mission progressed significant run-time penalty. Thedetail captured and
the correlationof the thermal model to flight data the quantity ofdata generatedby such a highfidelity
improved significantly. Since the thermalmodel and modelisnot possible usinga 1-dimensional model
limit lines were updated continuously basedon the alone. The3-dimensional model showed that the hot
correlations, confidence in the limit line chart increased spotswere not located near any of theflight thermal
dramatically during operations. sensors. It isbelieved that such a highfidelitymodel,
used earlier inthe designphase, could identify thehot
200 spots andbeused to place thermal sensorswhere they
190
are most needed. Also, the3-dimensional model
180
170 Orbit Pass 77 demonstrated that it could beused to evaluate and
160 Orbit Pass 99
150 Lower Corridor establish the thermal limit lines for the solar array in
140
130 Upper Corridor both the design andoperational phases. Byapplying
Temperature (°C)1110128900000 LILmaMRmAC eLd iLmiaimtite iL tA iLncientieon Line lpreersdosucocenesssd elwes athrhineleemdt hoaend deolvu deserianvlgel l qoeuxpaimsltieitnyng to tmfi mteheteh wothdaessr amdnraadlstmicoadlleyls
70 increased.
60
50
40
30 ACKNOWLEDGMENTS
20
10
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 The authorswould like to thank RichardKriegbaum of
Q dot(W/cm2)
Lockheed Martin Astronautics forprovidingdrawings,
Figure 13. Temperature as a functionof Q dotand
details of the assembly, and advice. Also, thanksgo out
orbit pass.
to theJPLnavigation team for giving us theopportunity
to make a contribution to thismission.Wewould also
In figure 13 there are two limit lines: one is a limit line
like to thank Mike Lindell forproviding supporting
based onthe NASALangley 3-dimensional finite
structural analysis.
element thermalmodel, and theother is the limit line
calculated by LockheedMartin’s 1-dimensionalmodel
8
American Institute of Aeronautics andAstronautics