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

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

Density

Slide 3

Mehta et al., 2011

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

Analytical Solution

Slide 5

wik

rkik

TTTT

,

,,b

iik kmvT3

2

, wb

irk T

kmvT )1(3

2

,

i

rksphereD T

Ts

serfssss

ssC ,

4

242

3

2

, 32)(

2144)exp(12

))exp()(1(

21)(1

211)exp(14 2

22

, ssserf

VVserf

ss

sDL

sC

i

rcylinderD

VrVi

23

1TwTi

1

xdttxerf

0

2 )exp(2)(

ibi Tk

mvs2

Sentman, 1961, Bird, 1994, Pilinski et al., 2011

DSMC DS3V

Slide 6

Energy Accommodation

Slide 7

io

io

TnKTnK

1

io

io

TnTn

17

17

1050.711050.7

Pilinski et al., 2010

Defined as the fraction of theenergy lost by free stream molecules on spacecraft surface impact

Gas Surface Interaction (GSI)

Sentman, 1961, Schamberg, 1959, Pilinski et al., 2011

Slide 8

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

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

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

GRACE

Slide 12

Altitude: 485 km at launch

Eccentricity: <0.005

Inclination: 89 deg

Mass: 432 kg

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

Grace: All Models

Slide 14

Slide 15

Grace: Mesh for DS3V

GRACE DSMC Results

Slide 16

July 19, 2005

GRACE DSMC Results compared with Sutton

Slide 17July 19, 2005

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

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

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

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

Questions?

Slide 22