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Slide 1
Satellite Drag Modeling using Direct Simulation Monte Carlo
(DSMC)
Piyush M. Mehta and Craig A. McLaughlinThe University of Kansas
Acknowledgement: Part of the work was done at the Los Alamos National Laboratory as part of the Space Weather Summer School
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Introduction Satellite Drag Model
Sources of error: Density, Drag Coefficient and Area Density Modeling:
Typically uses constant drag coefficient to derive densities from satellite data High Accuracy Satellite Drag Model (HASDM) uses drag coefficients varying with
altitude
Drag Coefficient Modeling: Orbit Prediction and Conjunction Analysis typically uses a constant drag coefficient
Slide 2
rel
relrel
Ddrag v
vv
mAC
a
2
21
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Density
Slide 3
Mehta et al., 2011
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Drag Coefficient Drag Coefficient is a strong function of:
Energy Accommodation (model) Gas Surface Interactions (GSI) (model) Attitude Surface Geometry Atmospheric Composition and Temperature (NRLMSISE-00) Surface Temperatures (Equations in Brown, AIAA Education Series, 2002) Spacecraft Relative Velocity
Slide 4
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Analytical Solution
Slide 5
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iik kmvT3
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irk T
kmvT )1(3
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,
i
rksphereD T
Ts
serfssss
ssC ,
4
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, 32)(
2144)exp(12
))exp()(1(
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22
, ssserf
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ss
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sC
i
rcylinderD
VrVi
23
1TwTi
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2 )exp(2)(
ibi Tk
mvs2
Sentman, 1961, Bird, 1994, Pilinski et al., 2011
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DSMC DS3V
Slide 6
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Energy Accommodation
Slide 7
io
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TnKTnK
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TnTn
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1050.711050.7
Pilinski et al., 2010
Defined as the fraction of theenergy lost by free stream molecules on spacecraft surface impact
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Gas Surface Interaction (GSI)
Sentman, 1961, Schamberg, 1959, Pilinski et al., 2011
Slide 8
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Results
Slide 9
150 200 250 300 350 400 450 5002.07
2.10
2.12
2.15
2.17
2.20
2.22
Spacecraft Surface Temperature, K
Dra
g C
oeffi
cien
t, C
D
600 700 800 900 1000 1100 1200 1300 14002.12
2.15
2.17
2.20
2.22
Free Stream Temperature, K
Dra
g C
oeffi
cien
t, C
D
Each data point is a DSMC simulation Each simulation take between 3-5 hrs
depending on the machine
Reference Simulation ConditionsTatm = 1157 KTsc = 300 KVr = 7590 m/sMolecular mass (m) = 11.35 amu
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Results
Slide 10
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 102.12
2.15
2.17
2.20
2.22
Spacecraft Relative Velocity, km/s
Dra
g C
oeffi
cien
t, C
D
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11.982.002.022.042.062.082.102.122.142.162.18
Analytical DSMC
Fraction of Specular Reflection
Dra
g C
oeffi
cien
t, C
D
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Results
Slide 11
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12
2.2
2.4
2.6
2.8
3
3.2Sphere
DSMC Analytical
Accommodation Coefficient, α
Dra
g C
oeffi
cien
t, C
D
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12.0
2.5
3.0
3.5
4.0
4.5
5.0Cylinder
A- L/D=1 D- L/D=1A- L/D=2 D - L/D = 2A- L/D = 3 D - L/D=3
Accommodation Coefficient, α
Dra
g C
oeffi
cien
t, C
D
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GRACE
Slide 12
Altitude: 485 km at launch
Eccentricity: <0.005
Inclination: 89 deg
Mass: 432 kg
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GRACE model for DSMC
Slide 13
Φ 3 deg 0 deg -3 degβ
0 deg 1.311 m2 1.004 m2 1.299 m2
-3 deg 1.335 m2 1.139 m2 1.323 m2
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Grace: All Models
Slide 14
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Slide 15
Grace: Mesh for DS3V
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GRACE DSMC Results
Slide 16
July 19, 2005
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GRACE DSMC Results compared with Sutton
Slide 17July 19, 2005
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Atmospheric PropertiesAccommodation
CoefficientHelium Number
DensityFree-Stream Temperature
Drag Components
Pressure -0.996 0.894 -0.848
Shear 0.900 -0.866 0.967
Drag Coefficient Modeling for GRACE
Slide 18
Correlation Coefficients
Data from July 19, 2005
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Various curve fits were use for both Pressure and Shear drag contributions
Additional simulations performed at random times to validate models. Error in using all the the models <1% More simulations need to be performed at different space weather
conditions for a complete model.
Slide 19
Drag Coefficient Modeling for GRACE
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Conclusion: Drag Coefficient Modeling The Direct Simulation Monte Carlo (DSMC) technique performed well in
explicitly calculating drag coefficients for satellites with simple (sphere and cylinder) and complex geometries with complete and partial accommodation.
Results show strong correlation of the total drag coefficient for a sphere with energy-accommodation, spacecraft relative velocity, and free-stream atmospheric temperature.
Drag coefficients can vary by more than 20% for complex geometries and by as much as 10% for a sphere along the satellite orbit. Therefore, use of a constant drag coefficient should be avoided in deriving densities from orbit data or for satellite conjunction.
Drag coefficients calculated by Sutton lie within the extreme cases of attitude simulated for GRACE. A high fidelity drag coefficient model for GRACE is highly feasible.
Slide 20
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Future Work Create and validate GRACE Drag Coefficient model Create Drag Coefficient Models for other satellites Use the drag coefficient model to update density models Work on ways to improve model fidelity
Slide 21
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Questions?
Slide 22